First slide

Scalars and Vectors

Question

If a vector $2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ is perpendicular to the vector $4 \hat{j} - 4 \hat{i} + α \hat{k}$ . Then the value of $α$ is

Easy

A

-1
B

$\frac{1}{2}$
C

$- \frac{1}{2}$
D

1

Solution

Given vectors can be rewritten as $\vec{A} = 2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ and $\vec{B} = - 4 \hat{i} + 4 \hat{j} + α \hat{k}$
Dot product of these vectors should be equal to zero because they are perpendicular.
$\begin{array}{l} ∴ \vec{A} \cdot \vec{B} = - 8 + 12 + 8 α = 0 \\ \Rightarrow 8 α = - 4 \\ \Rightarrow α = - 1 / 2 \end{array}$

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