If the projection of a = i -2 j +3 k on b =2 i + k is zero, then … - Vidyadip

MCQ

If the projection of $\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+\lambda\hat{\text{k}}$ is zero, then the value of $\lambda$ is:

A
$0$
B
$1$
✓
$\frac{-2}{3}$
D
$\frac{-3}{2}$

✓

Answer

Correct option: C.

$\frac{-2}{3}$

Since, two non zero vector $\vec{\text{a}}\ \&\ \vec{\text{b}}$ are i.e.,

$\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$

$\vec{\text{b}}=2\hat{\text{i}}+\lambda\hat{\text{k}}$

$\vec{\text{a}}.\vec{\text{b}}=0$

$(\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}).(2\hat{\text{i}}+\lambda\hat{\text{k}})=0$

$2+3\lambda=0$

$-2=3\lambda$

$\lambda=\frac{-2}{3}$

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