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If vecA = a hati+a hatj+b hatk and vecb ...

If `vecA = a hati+a hatj+b hatk` and `vecb = a hati - 2hatj - hatk` are perpendicular to other, then what is the minimum value that 'b' can have.

A

0

B

1

C

`-1`

D

b can have any value.

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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