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A non-zero vector vec a is such that it...

A non-zero vector ` vec a` is such that its projections along vectors `( hat i+ hat j)/(sqrt(2)),(- hat i+ hat j)/(sqrt(2))` and ` hat k` are equal, then unit vector along ` vec a` is a.`(sqrt(2) hat j- hat k)/(sqrt(3))` b. `( hat j-sqrt(2) hat k)/(sqrt(3))` c. `(sqrt(2))/(sqrt(3)) hat j+( hat k)/(sqrt(3))` d. `( hat j- hat k)/(sqrt(2))`

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Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i- hat j+ hat k is such that it is equally inclined to vec ba n d vec d where vec d= hat j+2 hat kdot The value of vec a is a. ( hat i+ hat j+ hat k)/(sqrt(2)) b. ( hat i- hat j+ hat k)/(sqrt(3)) c. (2 hat i+ hat j)/(sqrt(5)) d. (2 hat i+ hat j)/(sqrt(5))

A unit vector parallel to the intersection of the planes vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

The unit vector which is orthogonal to the vector 3 hat i+2 hat j+6 hat k and is coplanar with vectors 2 hat i+ hat j+ hat ka n d hat i- hat j+ hat k is (2 hat i-6 hat j+ hat k)/(sqrt(41)) b. (2 hat i-3 hat j)/(sqrt(13)) c. (3 hat j- hat k)/(sqrt(10)) d. (4 hat i+3 hat j-3 hat k)/(sqrt(34))

Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit vector vec c be coplanar. If vec c is perpendicular to vec a , then vec c is a. 1/(sqrt(2))(-hat j+hat k) b. 1/(sqrt(3))(-hat i-hat j-hat k)"" c. 1/(sqrt(5))(-hat k-2 hat j) d. 1/(sqrt(3))(hat i-hat j- hat k)

Let vec a= hat i- hat j , vec b= hat j- hat ka n d vec c= hat k- hat i. If vec d is a unit vector such that vec a.vec d=0=[ vec b vec c vec d], then d equals a. +-( hat i+ hat j-2 hat k)/(sqrt(6)) b. +-( hat i+ hat j- hat k)/(sqrt(3)) c. +-( hat i+ hat j+ hat k)/(sqrt(3)) d. +- hat k

The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 hat j+3 hat k . The unit vector parallel to one of the diagonals is a. 1/7(3 hat i+6 hat j-2 hat k) b. 1/7(3 hat i-6 hat j-2 hat k) c. 1/(sqrt(69))( hat i+6 hat j+8 hat k) d. 1/(sqrt(69))(- hat i-2 hat j+8 hat k)

If a vector vec(v) is such that 2 vec(v) + vec(v) xx [ hat(i) + 2 hat(j)] = 2 hat(i) + hat(k)and |vec(v)| = 1/3 sqrt(m) , then m is equal to -

If vec a.hat i= vec a.( hat i+ hat j)= vec a.( hat i+ hat j+ hat k) , then find the unit vector vec a

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

If the scalar projection of vector x hat i- hat j+ hat k on vector 2 hat i- hat j+5 hat k , is 1/(sqrt(30)) ,then find the value of xdot

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

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  2. Position vector hat k is rotated about the origin by angle 135^0 in...

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  3. A non-zero vector vec a is such that its projections along vectors ...

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  4. Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit v...

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  5. Let vec a=2i+j-2ka n d vec b=i+jdot If vec c is a vector such that ...

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  6. Let A B C D be a tetrahedron such that the edges A B ,A C and A D ar...

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  7. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i...

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  8. If vec a , vec b and vec c are non-coplanar unit vectors such that ...

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  9. Let vec u , vec v and vec w be vectors such that vec u+ vec v+ vec w...

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  10. If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecr...

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  11. Let vec pa n d vec q be any two orthogonal vectors of equal magnitu...

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  12. vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors an...

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  13. Find a unit vector perpendicular to each of the vectors ( vec a+ vec...

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  14. Prove that ( vec a.( vec bxx hat i)) hat i+( vec a.( vec bxx hat j)) h...

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  15. Column I, Column II The possible value of vec a if vec r=( hat i+ ha...

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  16. If vec A, vec B and vec C are vectors such that |vec B|=|vec C|. Prove...

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  17. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b...

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  18. Statement 1: Vector vec c=-5 hat i+7 hat j+2 hat k is along the bisec...

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  19. Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in...

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  20. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

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