Question

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

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(x2−x1,y2−y1,z2−z1) 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+2j−k).(2i+3j−6k)|2i+3j−6k| −4+6+6√22+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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