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If vec(a) and vec(b) are mutually perpen...

If `vec(a)` and `vec(b)` are mutually perpendicular unit vectors then `(3vec(a)+2vec(b)).(5vec(a)-6vec(b))=?`

A

3

B

5

C

6

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
Given`a^(2)=b^(2)=1 and vec(a).vec(b)=0`.
`:. (3vec(a)+2vec(b)).(5vec(a)-6vec(b))=15a^(2)-12b^(2)-8vec(a).vec(b)`
`=(15xx1)-(12xx1)-(8xx0)`
`=(15-12-0)=3`.
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RS AGGARWAL-PRODUCT OF THREE VECTORS-Objective Questions
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  3. If vec(a) and vec(b) are mutually perpendicular unit vectors then (3ve...

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  14. If vec a , vec b , and vec c are unit vectors such that vec a+ vec b...

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  15. If vec a ,\ vec b ,\ vec c are three mutually perpendicular unit ve...

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  17. Find the volume of the parallelepiped whose coterminous edges are r...

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  18. If the volume of a parallelepied having vec(a)=(5hat(i)-4hat(j)+hat(k)...

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  19. It is given that the vectorsvec(a)=(2hat(i)-2hat(k)), vec(b)=hat(i)+(l...

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