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Prove that vectors vec u=(a l+a1l1) hat...

Prove that vectors ` vec u=(a l+a_1l_1) hat i+(a m+a_1m_1) hat j+(a n+a_1n_1) hat k` ` vec v=(b l+b_1l_1) hat i+(b m+b_1m_1) hat j+(b n+b_1n_1) hat k` ` vec w=(c l+c_1l_1) hat i+(c m+c_1m_1) hat j+(c n+c_1n_1) hat k` are coplanar.

A

form an equilateral triangle

B

are coplanar

C

are collinear

D

are mutually perpendicular

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The correct Answer is:
B
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that vectors vec u=(a l+a1l1) hat i+(a m+a1m1) hat j+(a n+a1n1)...

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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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