Question

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

पर्याय

• 1

• 3

• 5

• 9

Answer 1

If the projection of ${\displaystyle 2\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}}}$ on ${\displaystyle \hat{\text{i}}+2\hat{\text{j}}+\alpha \hat{\text{k}}}$ is zero. Then, the value of α will be 5.

Explanation:

Here, ${\displaystyle \overrightarrow{\text{a}}.\overrightarrow{\text{b}}}$ = 0

∴ ${\displaystyle \overrightarrow{\text{a}}.\overrightarrow{\text{b}}=(2\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}}).(\hat{\text{i}}+2\hat{\text{j}}+\alpha \hat{\text{k}})}$ = 0

∴ 2 × 1 + 4 × 2 - 2 × α = 0

∴ α = 5