The values of a, for which the points A, B, C with position vectors 2 i - j + k, i - 3 j - 5 k and a i - 3 j + k respectively are the vertices of a right angled triangle with C = (π)/2 are:

Vector Algebra: JEE Main 2006 Mathematics question

JEE Main 2006 · Annual, Paper 1 · Q5761

JEE Main 2006Annual, Paper 1MathematicsMediumVector Algebra184× since 2002

The values of a, for which the points

A, B, C

with position vectors

2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k

and

a\widehat i - 3\widehat j + \widehat k

respectively are the vertices of a right angled triangle with

C = {\pi \over 2}

are :