A vector of magnitude `sqrt2` coplanar with the vectors `veca=hati+hatj+2hatk and vecb = hati + hatj + hatk,` and perpendicular to the vector `vecc = hati + hatj +hatk` is

Options

A. 0
B. 1
C. `-1`
D. b can have any value.

Answer

C

Explanation

If `vecA = ahatj+ahatj+bhatk` ………
If `vecA and vecB` are perpendicular
`vecA.vecB = 0 implies a^(2) - 2a - b = 0`
for a to have real rods
`D = (-2)^(2) - 4(1)(-b)ge0`
`implies 4+4b ge 0`
`implies b ge -1`
`:. B_(min) = -1`