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Two adjacent sides of a parallelogram ...

Two adjacent sides of a parallelogram `A B C D` are given by ` vec A B=2 hat i+10 hat j+11 hat ka n d vec A D=- hat i+2 hat j+2 hat kdot` The side `A D` is rotated by an acute angle `alpha` in the plane of the parallelogram so that `A D` becomes `A D^(prime)dot` If `A D '` makes a right angle with the side `A B ,` then the cosine of the angel `alpha` is given by a. `8/9` b. `(sqrt(17))/9` c. `1/9` d. `(4sqrt(5))/9`

A

`(8)/(9)`

B

`(sqrt(17))/(9)`

C

`(1)/(9)`

D

`(4sqrt(5))/(9)`

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The correct Answer is:
B
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Two adjacent sides of a parallelogram A B C D are given by vec A B=2 hat i+10 hat j+11 hat ka n d vec A D=- hat i+2 hat j+2 hat kdot The side A D is rotated by an acute angle alpha in the plane of the parallelogram so that A D becomes A D^(prime)dot If A D ' makes a right angle with the side A B , then the cosine of the angel alpha is given by 8/9 b. (sqrt(17))/9 c. 1/9 d. (4sqrt(5))/9

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