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Question

Find the projection of line joining (1, 2, 3) & (-1, 4, 2) on the line having direction ratios (2, 3 , -6) .
  1. =


Solution

The correct option is A
Projection of a vector a on another vector b is given by a.b|b|
Now we need to find vectors a & b
We have seen how to find the direction ratios of a line joining two points (x1,y1,z1) and (x2,y2,z2) It is given by(x2x1,y2y1,z2z1)
So we’ll have ,
Direction ratios of a =  (-1 -1  , 4 -2, 2 -3)
                              =  (-2, 2 , -1)
And thus the vector a will be given by,
                              a = -2i + 2j - k
And ,                     b =  2i + 3j - 6k
So, the projection of a on b =(2i+2jk).(2i+3j6k)|2i+3j6k| 4+6+622+32+62 (Using dot product of a and b)
=87
So, the projection of line segment joining (1, 2, 3) & (-1, 4, 2) on the line having direction ratios (2, 3 , - 6) = 87

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