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If veca, vecb and vecc1 are three non-co...

If `veca, vecb and vecc`1 are three non-coplanar vectors, then `(veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)]` equals

A

0

B

`[veca vecb vecc]`

C

`2[veca vecb vecc]`

D

`-[veca vecb vecc]`

Text Solution

Verified by Experts

The correct Answer is:
d
`(veca+ vecb+vecc).[(veca+vecb)xx(veca+vecc)]`
`= (veca+vecb+vecc).[veca xx veca +vecaxx vecc+vecb xx veca +vecbxxvecc]`
`= (veca +vecb +vecc).[veca xx vecc +vecb xx veca+vecb xxvecc]`
`[veca vecb vecc] -[veca vecb vecc]-[veca vecb vecc]`
`-[veca vecb vecc]`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. If |v...

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  3. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  4. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  5. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  6. Let vec a=2i+j+k , vec b=i+2j-k and a unit vector vec c be coplanar....

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  7. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  8. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  9. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  10. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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  11. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  12. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  13. Find the value of a so that the volume of the parallelepiped formed...

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  14. If veca=hati+hatj+hatk, veca.vecb=1 and veca xx vecb = hati-hatk, then...

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  15. The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hat...

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  16. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  17. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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  18. Let two non-collinear unit vector hat aa n d hat b form an acute a...

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  19. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  20. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

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