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Express the vector vec a=5 hat i-2 hat ...

Express the vector ` vec a=5 hat i-2 hat j+5 hat k` as the sum of two vectors such that one is parallel to the vector ` vec b=3 hat i+ hat k` and other is perpendicular to ` vec bdot`

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If vec a= hat i- 2 hat j and vec b= 2 hat i+ 2 hat j , find a unit vector parallel to the vector 3 vec a- 2 vec b .

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Find lambda if the vectors vec a=hat i-lambda hat j+3 hat k and vec b=4 hat i-5 hat j+2 hat k are perpendicular to each other.

Find the projection of the vector vec a = 2 hat i+ 3 hat j+ 2 hat k on the vector vec b= hat i+ 2 hat j+ hat k .

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For given vectors, vec a =2 hat i- hat j+2hat k and vec b =-hat i +hat j - hat k , find the unit vector in the direction of the vector vec a+ vec b .

Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Express the vector vec a=5 hat i-2 hat j+5 hat k as the sum of two ve...

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

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

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

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