The vector that must be added to the vector $$\hat i - 3\hat j + 2\hat k$$ and $$3\hat i - 6\hat j + 7\hat k$$ so that the resultant vector is a unit vector along the $$y$$-axis, is
A.
$$4\hat i - 2\hat j + 5\hat k$$
B.
$$ - 4\hat i - 2\hat j + 5\hat k$$
C.
$$3\hat i - 4\hat j + 5\hat k$$
D.
null vector
Answer :
$$ - 4\hat i - 2\hat j + 5\hat k$$
Solution :
Unit vector along $$y$$ axis = $${\hat j},$$ so the required vector
$$\eqalign{
& = \hat j - \left[ {\left( {\hat i - 3\hat j + 2\hat k} \right) + \left( {3\hat i + 6\hat j - 7\hat k} \right)} \right] \cr
& = - 4\hat i - 2\hat j + 5\hat k \cr} $$
Releted MCQ Question on Basic Physics >> Kinematics
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