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Let ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k` be three vectors. A vector ` vec v` in the plane of ` vec a a n d vec b ,` whose projection on ` vec c` is `1/(sqrt(3))` is given by a.` hat i-3 hat j+3 hat k` b. `-3 hat i-3 hat j+3 hat k` c. `3 hat i- hat j+3 hat k` d. ` hat i+3 hat j-3 hat k`

A

`hat(i)-3hat(j)+3hat(k)`

B

`-3hat(i)-3hat(j)-hat(k)`

C

`3hat(i)-hat(j)+3hat(k)`

D

`hat(i)+3hat(j)-3hat(k)`

Text Solution

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The correct Answer is:
C
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

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

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

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

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

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

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

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

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

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

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

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  12. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, find...

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  13. Let A be vector parallel to line of intersection of planes P1 and P2. ...

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  14. 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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  15. Find the 7th term of GP if the first term is 7 and common ratio is 2.

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  16. The unit vector which is orthogonal to the vector 3hati + 2hatj + 6hat...

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  17. The value of a so that the volume of parallelepiped formed by hat i...

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  18. If vec a=( hat i+ hat j+ hat k), vec a. vec b=1a n d vec axx vec b= h...

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  19. Let v=2hat(i)+hat(j)-hat(k) and w=hat(i)+3hat(k). If hat(u) is unit v...

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  20. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

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