First slide

Vectors

Question

If $\vec{A} = \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $\vec{B} = \hat{j} + \hat{k}$ are two vectors in space. Then find the cross product of the two vectors

Moderate

A

$5 \hat{i} - \hat{j} + \hat{k}$
B

$\hat{i} - 5 \hat{j} + \hat{k}$
C

$\hat{i} - \hat{j} + 5 \hat{k}$
D

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

Solution

$\vec{A} \times \vec{B} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & - 3 \\ 0 & 1 & 1 \end{matrix}| = \hat{i} (2 + 3) - \hat{j} (1 - 0) + \hat{k} (1 - 0) = 5 \hat{i} - \hat{j} + \hat{k}$

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