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Three vectors vecA=ahati+hatj+hatk, vecB...

Three vectors `vecA=ahati+hatj+hatk, vecB=hati+bhatj+hatk and vecC=hati+hatj+chatk` are mutually perpendicular `(hati,hatj and hatk` are unit vectors along X, Y, and Z axis respectively).
The respective values of a,b and c are

A

0,0,0

B

`-1/2,(-1)/2,(-1)/2`

C

1,-1,1

D

`1/2,1/2,1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
As `vecA, vecB and vecC` are perpendicular to each other,
` vecA*vecB=vecB*vecC=vecC*vecA=0`
`therefore a+b+1=1+b+c=a+1+c=0`
a+b+1=0…. (1)
1+b+c=0 …..(2)
a+1+c=0…. (3)
Solving equations (1), (2) and (3) we get,
`1=b=c=(-1)/(2)`
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