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Geometry Level pending

Find the length of the perpendicular drawn from the point ( 3 , − 1 , 11 ) (3,-1,11) to the line x 2 = y − 2 3 = z − 3 4 \dfrac{x}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} .

33 \sqrt{33} 66 \sqrt{66} 53 \sqrt{53} 29 \sqrt{29}

Ppk K by ppk k , 20, India

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1 solution

Ppk K
Feb 12, 2017

Let the coordinates of Q be (2w, 3w+2, 4w+3) which is any point on the straight line AB.

Therefore, DR's of PQ is (2w-3, 3w+3, 4w-8)

And also perpendicular to the straight line AB=w having DR's (2,3,4).

Thus equating the equation to 0 aand solving it we get w=1 and co-ordinates of Q are (2,5,7).

Hence magnitude of PQ= root 53

Enjoy learning !!!!!

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