If = -4 î - 2 ĵ - 3
, what is
× ĵ ?

Question

If  = -4 î - 2 ĵ - 3 
, what is 
× ĵ ?

Quizplus · Accepted Answer

Assuming that each set of alphanumeric characters denotes a vector, we can equate the given equation to:
-4 î - 2 ĵ - 3(11ea98f3_0f6d_cbd1_99aa_d5fec761f528_TB2997_11) = 11ea98f3_0f6d_a4c0_99aa_971b9dbc992b_TB2997_11
Simplifying, we get:
(33 î - 6 ĵ) = 33(11ea98f3_0f6d_cbd1_99aa_d5fec761f528_TB2997_11)
Dividing by 33, we get:
î - (2/11)ĵ = 11ea98f3_0f6d_cbd1_99aa_d5fec761f528_TB2997_11

Now, to find the cross product of 11ea98f3_0f6d_cbd2_99aa_41ef8bdb7a18_TB2997_11 and ĵ, we can form the determinant:
| î     ĵ     k   |
| 1      -2/11  0  |
| 0      x     0  |
Expanding along the second row, we get:
-1(0-0) - (-2/11)(0-x) + 0(0-x) = -2x/11
Thus, the answer is 3 î - 4(11ea98f3_0f6d_cbd3_99aa_45098d0c206c_TB2997_11) = 3 î - (8/11)ĵ = 11ea98f3_0f6d_cbd2_99aa_41ef8bdb7a18_TB2997_11 x ĵ. 
This matches with option A.