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Let vecA be a vector parallel to the lin...

Let `vecA` be a vector parallel to the line of intersection of planes `P_(1) and P_(2)` . Plane `P_(1)` is parallel to vectors `2hatj + 3hatk and 4hatj - 3hatk nad P_(2) " is parallel to " hatj- hatk and 3hati + 3hatj`. Then the angle between vector `vecA and ` a given vector `2hati + hatj - 2hatk` is

A

`pi//2`

B

`pi//4`

C

`pi//6`

D

`3pi//4`

Text Solution

Verified by Experts

The correct Answer is:
b,d
Normal to plane `P_(1)` is
`vecn_(1)= (2hatj+3hatk)xx)(4hatj-3hatk)=-18hati`
Normal to plane `P_(2)` is
Therefore, `vecn_(2)= (hatj-hatk)xx (3hati +3hatj)=3hati -3hatj-3hatk`
`vecA` is parallel to `+-(vecn_(1)xx vecn_(2))=+- (-54hatj+54hatk)`
Now , the angle between `vecA nad 2hati +hatj - 2hatk` is given by
`cos thet=+-((-54hatj+54hatk).(2hati+hatj-2hatk))/(54sqrt2 .3)`
`=+-1/sqrt2`
`theta= pi//4 or 3pi//4`
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