Question 27: Motion in 2D & Vectors

Question

If the projection of $$2 \hat{i}+4 \hat{j}-2 \hat{k}$$ on $$\hat{i}+2 \hat{j}+\alpha \hat{k}$$ is zero. Then, the value of $$\alpha$$ will be ___________.

Accepted Answer

$$\overrightarrow A  = 2\widehat i + 4\widehat j - 2\widehat k$$
$$\overrightarrow B  = \widehat i + 2\widehat j + \alpha \widehat k$$
$$\overrightarrow A \,.\,\overrightarrow B  = 0$$, as $$\overrightarrow A $$ should be perpendicular to $$\overrightarrow B $$
$$ \Rightarrow 2 + 8 - 2\alpha  = 0$$
$$\alpha  = 5$$

Motion in 2D & Vectors

If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k} on \hat{i}+2 \hat{j}+\alpha \hat{k} is zero. Then, the value of \alpha$ will be ___________.

Integer / Numeric Answer Type