SATHEE: Kinematics Question 259

Kinematics Question 259

Question: If $\vec{A} = 3 \hat{i} + \hat{j} + 2 \hat{k}$ and $\vec{B} = 2 \hat{i} - 2 \hat{j} + 4 \hat{k}$ then value of $| \vec{A} \times \vec{B} |$ will be

Options:

A) $8 \sqrt{2}$

B) $8 \sqrt{3}$

C) $8 \sqrt{5}$

D) $5 \sqrt{8}$

Show Answer

Answer:

Correct Answer: B

Solution:

$\vec{A} \times \vec{B} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 1 & 2 \\ 2 & - 2 & 4 \end{matrix} |$

$= (1 \times 4 - 2 \times - 2) \hat{i} + (2 \times 2 - 4 \times 3) \hat{j} + (3 \times - 2 - 1 \times 2) \hat{k}$

$= 8 \hat{i} - 8 \hat{j} - 8 \hat{k}$

Magnitude of $\vec{A} \times \vec{B} = | \vec{A} \times \vec{B} | = \sqrt{{(8)}^{2} + {(- 8)}^{2} + {(- 8)}^{2}}$

$= 8 \sqrt{3}$

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