First slide

Vectors

Question

Determine a vector which when added to the resultant of $\vec{A} = 2 \hat{i} + 5 \hat{j} - \hat{k}$ and $\vec{B} = 3 \hat{i} - 4 \hat{j} - \hat{k}$ gives unit vector along negative y direction.

Moderate

A

$- 5 \hat{i} - 2 \hat{j} + 2 \hat{k}$
B

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

$- 5 \hat{i} - \hat{j} + 2 \hat{k}$
D

$5 \hat{i} - \hat{j} + 2 \hat{k}$

Solution

Let $\vec{C}$ is required vector, then $\vec{C} + \vec{A} + \vec{B} = - \hat{j}$
$\Rightarrow$ $\vec{C} + 2 \hat{i} + 5 \hat{j} - \hat{k} + 3 \hat{i} - 4 \hat{j} - \hat{k} = - \hat{j}$
$\Rightarrow \vec{C} = - 5 \hat{i} - 2 \hat{j} + 2 \hat{k}$

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