If the vector a=i-j+2k , b=2i+4j+k and c= i+j+ k are mutually ort… - Vidyadip

MCQ

If the vector $\vec a=i-j+2k ,\vec b=2i+4j+k $ and $\vec c=$ $\alpha i+j+\beta k$ are mutually orthogonal then $(\alpha ,\beta ) =$

A
$(2,-3)$
B
$(-2,3)$
C
$(3,-2)$
✓
$(-3,2)$

✓

Answer

Correct option: D.

$(-3,2)$

d
$ \vec{a}=\hat{i}-\hat{j}+2 \hat{k}, $

$\vec{b}=2 \hat{i}+4 \hat{j}+4 \hat{k} ,$

$\vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k} $

$\vec{a}$ and $\vec{c}$ are orthogonal $\Rightarrow \vec{a} \cdot \vec{c}=0$ giving $\lambda-1+2 \mu=0$

Also $\vec{b}$ and $\vec{c}$ are orthogonal $\Rightarrow 2 \lambda+4+4 \mu=0$

Solving the equation we get $\lambda=-3, \mu=2$

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