In a triangle ABC, right angle at vertex A, if the position vectors of A, B and C are respectively 3 i+ j- k, - i+3 j+p k and 5 i+q j-4 k, then the point (p,q) lies on a line:

JEE Main 2016 Mathematics question

In a triangle , right angle at vertex , if the position vectors of , and are respectively , and , then the point lies on a line:

Answer: (4)

Form the two vectors emanating from the right-angled vertex:

= -4 i+2 j+(p+1) k, = 2 i+(q-1) j-3 k.

A right angle at means these are perpendicular, so their dot product vanishes:

-8 + 2(q-1) - 3(p+1) = 0

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Question ID VK-115580