Q.

The distance of the point (−1,−5,−10) from the point of intersection of the line r¯=2i¯−j¯+2k¯+λ(3i¯+4j¯+2k¯) and plane r¯.(i¯−j¯+k¯)=5 is

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answer is 13.

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Detailed Solution

Equation of line x−23=y+14=z−22 a point on the line it lies on the plane x-y+z=5p(2,−1,2)Q(−1,−5,−10)PQ=9−16+144=13
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The distance of the point (−1,−5,−10) from the point of intersection of the line r¯=2i¯−j¯+2k¯+λ(3i¯+4j¯+2k¯) and plane r¯.(i¯−j¯+k¯)=5 is