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If veca=xhati + y hatj + zhatk, vecb= yh...

If `veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk ` and `vecc= zhati + xhatj+ yhatk `, `" then " vecaxx (vecbxx vecc) `is
(a)parallel to ` ( y- z) hati + (z - x) hatj + (x -y) hatk` (b)orthogonal to `hati + hatj + hatk` (c)orthogonal to ` ( y+z) hati + ( z + x) hatj + ( x + y) hatk` (d)orthogonal to `xhati + yhatj + zhatk`

A

parallel to `(y-z)hati+(z-x)hatj+(x-y)hatk`

B

orthogonal to `hati+hatj+hatk`

C

orthogonal to `(y+z)hati+(z+x)hatj+(x+y)hatk`

D

parallel to `hati+hatj+hatk`

Text Solution

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The correct Answer is:
A, B, C
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

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  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

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  3. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

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  4. Let O be the origin, and O X , O Y , O Z be three unit vectors ...

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  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

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  6. Let vec a , vec b and vec c be three non-zero vectors such that no ...

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  7. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

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  8. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

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  9. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

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

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  11. Let P,Q R and S be the points on the plane with position vectors -2hat...

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  12. If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sq...

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

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  14. The edges of a parallelopiped are of unit length and are parallel to ...

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  15. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

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  16. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

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  17. The number of distinct real values of lambda , for which the vectors...

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  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

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  19. Let vec A be a vector parallel to the line of intersection of plan...

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  20. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

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  21. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

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