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If the two adjacent sides of two rect...

If the two adjacent sides of two rectangles are represented by vectors ` vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec ba n d vec r=-4 vec a- vec b ; vec s=- vec a+ vec b ,` respectively, then the angel between the vector ` vec x=1/3( vec p+ vec r+ vec s)a n d vec y=1/5( vec r+ vec s)` is `cos^(-1)((19)/(5sqrt(43)))` b. `cos^(-1)((19)/(5sqrt(43)))` c. `picos^(-1)((19)/(5sqrt(43)))` d. cannot be evaluate

A

`pi-cos^(-1)((19)/(5sqrt(43)))`

B

`cos^(-1)((19)/(5sqrt(43)))`

C

`-cos^(-1)((19)/(5sqrt(43)))`

D

`pi-cos^(-1)((19)/(sqrt(43)))`

Text Solution

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The correct Answer is:
B
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If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec ba n d vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s)a n d vec y=1/5( vec r+ vec s) is a.cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. picos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

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