SATHEE: Kinematics Question 5

Kinematics Question 5

Question: $\vec{A} = 2 \hat{i} + \hat{j}, B = 3 \hat{j} - \hat{k}$ and $\vec{C} = 6 \hat{i} - 2 \hat{k}$ . Value of $\vec{A} - 2 \vec{B} + 3 \vec{C}$ would be

Options:

A) $20 \hat{i} + 5 \hat{j} + 4 \hat{k}$

B) $20 \hat{i} - 5 \hat{j} - 4 \hat{k}$

C) $4 \hat{i} + 5 \hat{j} + 20 \hat{k}$

D) $5 \hat{i} + 4 \hat{j} + 10 \hat{k}$

Show Answer

Answer:

Correct Answer: B

Solution:

$\vec{A} - 2 \vec{B} + 3 \vec{C} = (2 \hat{i} + \hat{j}) - 2 (3 \hat{j} - \hat{k}) + 3 (6 \hat{i} - 2 \hat{k})$

$= 2 \hat{i} + \hat{j} - 6 \hat{j} + 2 \hat{k} + 18 \hat{i} - 6 \hat{k}$ = $20 \hat{i} - 5 \hat{j} - 4 \hat{k}$

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