The vector product of two vectors A =2 hat i + hat j - hat k and B =- hat i - hat j +2 hat k is

Question

The vector product of two vectors A =2 hat i + hat j - hat k and B =- hat i - hat j +2 hat k is (A) 2 hat i +3 hat j - hat k  (B)  hat i +3 hat j + hat k  (C) - hat i +3 hat j +2 hat k  (D)  hat i -3 hat j - hat k

Tardigrade Admin · Accepted Answer

Given, A =2 hat i + hat j - hat k , B =- hat i - hat j +2 hat k ∴ Vector product, A × B =| hat i hat j hat k 2 1 -1 -1 -1 2| = hat i (2-1)- hat j (4-1)+ hat k (-2+1)= hat i -3 hat j - hat k

Q. The vector product of two vectors $A = 2 \hat{i} + \hat{j} - \hat{k}$ and $B = - \hat{i} - \hat{j} + 2 \hat{k}$ is

$2 \hat{i} + 3 \hat{j} - \hat{k}$

$\hat{i} + 3 \hat{j} + \hat{k}$

$- \hat{i} + 3 \hat{j} + 2 \hat{k}$

$\hat{i} - 3 \hat{j} - \hat{k}$

Given, $A = 2 \hat{i} + \hat{j} - \hat{k}, B = - \hat{i} - \hat{j} + 2 \hat{k}$
$∴$ Vector product, $A \times B = ∣ ∣ \hat{i} 2 - 1 \hat{j} 1 - 1 \hat{k} - 1 2 ∣ ∣$
$= \hat{i} (2 - 1) - \hat{j} (4 - 1) + \hat{k} (- 2 + 1) = \hat{i} - 3 \hat{j} - \hat{k}$

Q. The vector product of two vectors A=2i^+j^​−k^ and B=−i^−j^​+2k^ is

2i^+3j^​−k^

i^+3j^​+k^

−i^+3j^​+2k^

i^−3j^​−k^