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A unit vector in the direction of result...

A unit vector in the direction of resultant vector of `vecA = -2hati + 3hatj + hatk and vecB = hati + 2 hatj - 4 hatk` is

A

`(-2hati+3hatj+hatk)/(sqrt(35))`

B

`(hati+2hatj-4hatk)/(sqrt(35))`

C

`(-hati+5hatj-3hatk)/(sqrt(35))`

D

`(-3hati+hatj+5hatk)/(sqrt(35))`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `vecA = -2hati + 3hatj + hatj`
`vecB = hati + 2hatj - 4hatk`
The resultant vector `vecA and vecB` is `vecR = vecA + vecB`
`therefore vecR = (-2hati + 3hatj + hatk) + (hati + 2hatj - 4hatk) = -hati + 5hatj - 3hatk`
`|vecR | = sqrt((-1)^(2) + (5)^(2) + (-3)^(2)) = sqrt(1+25 + 9) = sqrt(35)`
Unit vector in the direction of resultant vector of `vecA and vecB` is
`hatR = (vecR)/(|vecR|) = (-hati + 5hatj - 3hatk)/(sqrt(35))`
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