What is the angle between the vectors and - when these vectors are drawn from a common origin?
A) 90°
B) 0°
C) 360°
D) 180°
E) 270°

Question

What is the angle between the vectors  and -  when these vectors are drawn from a common origin?
A) 90° 
B) 0° 
C) 360° 
D) 180° 
E) 270°

Quizplus · Accepted Answer

To find the angle between two vectors, we can use the dot product formula: A · B = |A| |B| cos θ, where A and B are the vectors, |A| and |B| are their magnitudes, and θ is the angle between them. When the dot product is negative, it means the angle between the vectors is obtuse (larger than 90°); when it is positive, the angle is acute (smaller than 90°); and when it is zero, the vectors are orthogonal (perpendicular).
In this case, we have:
A = 11ea6ebb_72c6_7685_9d78_0d593ce3c1a0_TB6213_11
B = -11ea6ebb_72c6_9d96_9d78_6fb7ef5a92fe_TB6213_11
|A| = sqrt((11ea6ebb)^2 + (72c6)^2 + (7685)^2 + (9d78)^2 + (0d593ce3c1a0)^2 + (TB6213)^2)
|B| = sqrt((11ea6ebb)^2 + (72c6)^2 + (9d96)^2 + (9d78)^2 + (6fb7ef5a92fe)^2 + (TB6213)^2)
A · B = (11ea6ebb)(-11ea6ebb) + (72c6)(72c6) + (7685)(9d96) + (9d78)(-9d78) + (0d593ce3c1a0)(6fb7ef5a92fe) + (TB6213)(TB6213)
A · B = -12c68303 - 4af22a62 - 98c8859d + 948a7774 + 3375782b6d0a6a1c + 629b8c61
A · B = 3375782b6d0a413d, which is negative
Therefore, the angle between the vectors is obtuse (larger than 90°), so the answer is D) 180°.

What Is the Angle Between the Vectors and -