if the vectors `P = alphahati+alphaj+3hatk` and `Q = alphahati - 2 hatj - hatk` are perpendicular to each other, then the positive value of `alpha` is

Options

A. zero
B. `1`
C. `2`
D. `3`

Answer

d

Explanation

The scalar praduct of two vectors is given by
`overset(vec)(P) .overset(vec)(Q) = PQ cos theta`
where `theta` is angle between them
Given , `hatP = a hati + a hat j + 3hatk,vecQ = a hati - 2 hatj - hatk`
`theta 90^(@)`
`:. vecP . vecQ = PQ cos 90^(@) = 0`
`(a hati - hatj -3 hatk).(a hati - 2 hatj - hatk) = 0`
`a^(2) - 2a - 3 = 0`
`rArr a = (2 +- sqrt(4 + 12))/(2) = 3 = 1`
Hence position value of a is `3`.