Let a=j -k and c= i -j -k Then the vector b satisfying a b + c = … - Vidyadip

MCQ

Let $\vec a=j -k $ and $ \vec c= i -j -k $ Then the vector $\vec b$ satisfying $\vec a \times \vec b + \vec c = 0$ and $\vec a\cdot \vec b=3 $

A
$2i -j +2k$
B
$i -j -2k$
C
$i+j-2k$
✓
$-i+j-2k$

✓

Answer

Correct option: D.

$-i+j-2k$

d
let $\vec{b}=x \vec{i}+y \vec{j}+z \vec{k}$

${\text {given}, \vec{a} \cdot \vec{b}=3}$

${\Rightarrow y-z=3 \ldots \ldots(1)} $

${\text { Also, }(\vec{a} \times \vec{b})+\vec{c}=0} $

${\Rightarrow(z+y) \vec{i}-x \vec{j}-x \vec{k}+\vec{i}-\vec{j}-\vec{k}=0} $

${\Rightarrow(z+y+1) \vec{i}-(x+1) \vec{j}-(x+1) \vec{k}=0}$

${\Rightarrow x+1=0 \Rightarrow x=-1} $

${\text { and } z+y+1=0 \Rightarrow y+z=-1 \quad \cdots \cdots(2)} $

${\text { solving equation }(1) \text { and }(2) \text { we get, }}$

$y=1$ and $z=-2$

hence $\vec{b}=-1 \vec{i}+1 \vec{j}-2 \vec{k}$

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