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What is the angle between two vectors 2 ...

What is the angle between two vectors `2 vec i+3vecj+veck and -3vec i+6vec k` ?

A

`60^(@)`

B

`0^(@)`

C

`45^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec P = 2hati + 3hatj + hatk and vec Q =-3hati +6hatk`
`therefore vec P cdot vec Q = PQ cos theta`
`therefore cos theta =(vec P cdot vec Q)/(PQ) =((2hati + 3hatj+hatk) cdot (-3hati + 6hatk))/((sqrt(4+9+1))xx sqrt((9+36))`
`therefore cos theta =(-6+0+6)/(sqrt(14) sqrt(45))=0`
`therefore cos theta =0^(@)" "therefore theta =90^(@)`
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MARVEL PUBLICATION-VECTORS-MULTIPLE CHOICE QUESTIONS (STANDARD LEVEL)
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  2. A force (3 hat(i)+4 hat(j)) acts on a body and displaces it by (3 hat(...

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  3. A particle moves with a velocity of 6hati-4hatj+3hatk m//s under the a...

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  4. A force vec F=(2hati+2hatk) N displaces a body by an amount vec S=(2ha...

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  5. vec P and vec Q are two perpendicular vectors. If vec P = 5 hati +7hat...

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  6. What is the angle between two vectors 2 vec i+3vecj+veck and -3vec i+6...

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  7. Under a force (10hati-3hatj+6hatk) newton a body of mass 5 kg moves fr...

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  8. What is the work done when a force vec F =2hati +3hatj-5hatk units act...

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  9. What is the anlge between vec P xx vec Q and vec Q xx vec P is

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  10. If |vec P xx vec Q|=PQ then the angle between vec P and vec Q is

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  11. If |vec P xx vec Q|=PQ then the angle between vec P and vec Q is

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  12. The magnitude of the vector product of two vectors is sqrt(3) times th...

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  13. Two vectors vec P and vec Q of the same type with tails at a point O a...

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  14. You are given two vectors vec P=2hati-3hatj-hatk and vec Q =-6hati+9ha...

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  15. If vec A cdot vec B =0 and vec A xx vec C=0, then the angle between B ...

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  16. The linear velocity of a particle on a rotating body is given by vec v...

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  17. The torque of the force vecF=(2hati-3hatj+4hatk)N acting at the point ...

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  18. O is the centre of an equilateral triangle ABC. vec F(1), vec F(2) and...

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  19. If vec(A) xx vec(B) = vec(B) xx vec(A), then the angle between A to B ...

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  20. If vec(a) and vec(b) are two vectors then the value of (vec(a) + vec(b...

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