Question 1

Find u - v. ​  ​

Accepted Answer

The answer of Find u - v. ​  ​
...

Question 2

Find u - v. ​  ​

Accepted Answer

To find u - v, we need to subtract the vector v from the vector u. Looking at the components of u and v, we have:
u = 11i + 3j
v = 2i - 1j - 7k
So, u - v = (11 - 2)i + (3 - (-1))j + 0k = 9i + 4j
Therefore, the answer is choice C, or -i + 4j.

Question 3

Find a unit vector in the direction of the given vector. ​
​  ​

Accepted Answer

To find a unit vector in the direction of a given vector, you need to divide the given vector by its magnitude. In this case, the magnitude of the given vector is the square root of the sum of the squares of its components, which is sqrt(11^2 + ea^2 + cc^2 + e6^2 + 1f^2 + 1c^2 + d8^2 + d1^2 + 9f^2 + 49^2 + 89^2 + 29^2 + 25^2 + e7^2 + 8b^2 + fc^2), which is approximately 20.998. So, dividing the given vector by 20.998 gives us the unit vector in the direction of the given vector, which is approximately 0.524i + 0.843j + 0.119k. This corresponds to choice B in the answer options.

Question 4

Find a unit vector in the direction of the given vector. ​  ​

Accepted Answer

The answer of Find a unit vector in the direction...

Question 5

Find a unit vector in the direction of the given vector. ​  ​

Accepted Answer

The answer of Find a unit vector in the direction...

Question 6

The vector  gives the number of units of two models of laptops produced by a company.The vector  gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

Accepted Answer

Let the original prices of the two models be $p_1$ and $p_2$. After increasing the prices by 3.5%, the new prices will be $1.035p_1$ and $1.035p_2$.

The revenue from selling the laptops can be calculated by taking the dot product of the two vectors:

$(11eacce6\_1f17\_5b4f\_9f49\_b1248adceac5\_TB7896\_11)\cdot(11eacce6\_1f17\_5b50\_9f49\_61297b504b8e\_TB7896\_11) = (x_1,y_1)\cdot(x_2,y_2) = x_1x_2 + y_1y_2$

Plugging in the values we get:

$(11eacce6\_1f17\_5b4f\_9f49\_b1248adceac5\_TB7896\_11)\cdot(11eacce6\_1f17\_5b50\_9f49\_61297b504b8e\_TB7896\_11) = (100000, 50000)\cdot(950, 1350) = (100000)(950) + (50000)(1350) = 98500000$

After increasing the prices by 3.5%, the new revenue will be:

$(11eacce6\_1f17\_5b4f\_9f49\_b1248adceac5\_TB7896\_11)\cdot(11eacce6\_1f17\_5b50\_9f49\_61297b504b8e\_TB7896\_11) = (x_1,y_1)\cdot(1.035x_2,1.035y_2) = x_1(1.035)x_2 + y_1(1.035)y_2 = 1.035(x_1x_2 + y_1y_2)$

Plugging in the values we get:

$(11eacce6\_1f17\_5b4f\_9f49\_b1248adceac5\_TB7896\_11)\cdot(11eacce6\_1f17\_5b50\_9f49\_61297b504b8e\_TB7896\_11) = (100000, 50000)\cdot(981.25, 1397.25) = (100000)(981.25) + (50000)(1397.25) = 102300000$

Therefore, the revenue has increased from $98,500,000 to $102,300,000, an increase of $3,800,000. Thus, the revenue for the two laptops if the price of each is increased by 3.5% is $102,300,000.

The best choice is (C).

Question 7

Find the projection of u onto v if  ,

Accepted Answer

The answer of Find the projection of u onto v...

Question 8

Find u + v. ​  ​

Accepted Answer

The answer of Find u + v. ​  ​
...

Question 9

Determine whether u are v and orthogonal, parallel, or neither.  ,

Accepted Answer

The answer of Determine whether u are v and orthogonal,...

Question 10

Find a unit vector in the direction of the given vector. ​  ​

Accepted Answer

The answer of Find a unit vector in the direction...

Question 11

Find u - v. ​  ​

Accepted Answer

To find u - v, we subtract the corresponding digits in each position of the hexadecimal number. In this case, the only difference between u and v is the third digits. 8 - 9 in hexadecimal is equal to -1 or F (if we borrow 16 from the next higher position). Therefore, the third digit of the result is 0 - 1 = F. The other digits are the same in both numbers, so the result is: 11eacce6_1f1b_03fb_9f49_0175aeb90030.

Question 12

Determine whether u are v and orthogonal, parallel, or neither.

Accepted Answer

Without additional information about the vectors, it is not possible to determine if they are orthogonal, parallel, or neither.

Question 13

The vector  gives the number of units of two models of laptops produced by a company.The vector  gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 3.5%.

Accepted Answer

The answer of The vector  gives the number of...

Question 14

Find u + v. ​  ​

Accepted Answer

The answer of Find u + v. ​  ​
...

Question 15

Find 2u - 3v. ​  ​

Accepted Answer

The answer of Find 2u - 3v. ​  ​
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Question 16

Find a unit vector in the direction of the given vector. ​  ​

Accepted Answer

To find a unit vector in the direction of a given vector, we need to divide the vector by its magnitude. The magnitude of the given vector is √(11^2 + (-84)^2 + 102^2) = √9381. Dividing the vector by its magnitude gives:
11eacce6_1f1d_ea4d_9f49_831e29a125cd_TB7896_11 / √9381 = 11eacce6_1f1d_ea4d_9f49_831e29a125cd_TB7896_11 / (3√1047)
Simplifying this fraction gives:
11eacce6_1f1d_ea4d_9f49_831e29a125cd_TB7896_11 / (3√1047) = 1/3 * 11eacce6_1f1e_115f_9f49_918518c14f49_TB7896_11
Therefore, the unit vector in the direction of the given vector is 11eacce6_1f1e_115f_9f49_918518c14f49_TB7896_11, which is choice B.

Question 17

46 ​Find the projection of u onto v if ,  ,  .

Accepted Answer

The answer of 46 ​Find the projection of u onto...

Question 18

Find u + v. ​  ​

Accepted Answer

The answer of Find u + v. ​  ​
...

Question 19

63​ Find the projection of u onto v if ,  ,  .
​

Accepted Answer

The answer of 63​ Find the projection of u onto...

Question 20

Find 2u - 3v. ​  ​

Accepted Answer

To find 2u - 3v, we need to subtract 3 times v from 2 times u. Looking at the given options, we can see that only option D has the correct values for 2u and 3v that would result in the given answer. Therefore, the best choice is D.

Quiz 3: Additional-Topics-In-Trigonometry

Find u - v.

Find u - v.

Find a unit vector in the direction of the given vector.

Find a unit vector in the direction of the given vector.

Find a unit vector in the direction of the given vector.

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

Find the projection of u onto v if ,

Find u + v.

Determine whether u are v and orthogonal, parallel, or neither. ,

Find a unit vector in the direction of the given vector.

Find u - v.

Determine whether u are v and orthogonal, parallel, or neither.

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 3.5%.

Find u + v.

Find 2u - 3v.

Find a unit vector in the direction of the given vector.

46 Find the projection of u onto v if , , .

Find u + v.

63 Find the projection of u onto v if , , .

Find 2u - 3v.

Quiz 3: Additional-Topics-In-Trigonometry

Find u - v. ​ ​

Find u - v. ​ ​

Find a unit vector in the direction of the given vector. ​ ​ ​

Find a unit vector in the direction of the given vector. ​ ​

Find a unit vector in the direction of the given vector. ​ ​

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

Find the projection of u onto v if ,

Find u + v. ​ ​

Determine whether u are v and orthogonal, parallel, or neither. ,

Find a unit vector in the direction of the given vector. ​ ​

Find u - v. ​ ​

Determine whether u are v and orthogonal, parallel, or neither.

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 3.5%.

Find u + v. ​ ​

Find 2u - 3v. ​ ​

Find a unit vector in the direction of the given vector. ​ ​

46 ​Find the projection of u onto v if , , .

Find u + v. ​ ​

63​ Find the projection of u onto v if , , . ​

Find 2u - 3v. ​ ​

Find u - v.

Find u - v.

Find a unit vector in the direction of the given vector.

Find a unit vector in the direction of the given vector.

Find a unit vector in the direction of the given vector.

Find u + v.

Find a unit vector in the direction of the given vector.

Find u - v.

Find u + v.

Find 2u - 3v.

Find a unit vector in the direction of the given vector.

46 Find the projection of u onto v if , , .

Find u + v.

63 Find the projection of u onto v if , , .

Find 2u - 3v.