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If a, b, c are then p^(th),q^(th),r^(t...

If `a, b, c` are then `p^(th),q^(th),r^(th)`, terms of an HP and `vec u=(q-r)hat i+(r-p)hat j+(p-q)hat k and vec v=hat i/a+hat j/b+hat k/c` then

A

`vec(u) , vec(v)` are parallel vectors

B

`vec(u) , vec(v)` are orthogonal vectors

C

`vec(u), vec(v)` = 1

D

`vec(u) xx vec(v) = hat(i) + hat(j) + hat(k)`

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The correct Answer is:
B
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MOTION-VECTOR -EXERCISE - 2 ( LEVEL -I)
  1. Image of the point P with position vector 7hat(i) - hat(j) + 2hat(k)...

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  2. If a, b, c are then p^(th),q^(th),r^(th), terms of an HP and vec u=...

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  3. If the unit vectors vec(e(1)) and vec(e(2)) are inclined at an ang...

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  4. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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  5. Let vec(u) = hat(i) + hat(j), vec(v) = hat(i) - hat(j) and vec(w) = h...

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  6. In a quadrilateral ABCD. vec(AC) is the bisector of vec(AB) and vec(...

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  7. If vec a =vec b +vec c,vec b xx vec d =vec 0 ,vec c *vec d = 0 then ...

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  8. Consider a tetrahedron with faces f1, f2, f3, f4. Let vec a1, vec a2...

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  9. Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(...

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  10. Points L, M and N lie on the sides AB, BC and CA of the triangle ABC s...

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  11. For any four points P,Q,R,S |bar(PQ) xx bar(RS) - bra(QR) xx bar(PS) ...

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  12. Given vec(a) = xhat(i) + yhat(j) + 2hat(k) , vec(b) = hat(i) - hat(j)...

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  13. Let vec r be a vector perpendicular to vec a + vec b+ vec c, where [ve...

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  14. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equal...

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  15. If the vectors a hat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k) and hat(i...

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  16. (vec(d) + vec(a)).(vec(a) xx (vec(b) xx (vec(c) xx vec(d)))) simplifie...

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  17. [(vec(a) xx vec(b)) xx (vec(b) xx vec(c)), (vec(b) xx vec(c)) xx (vec(...

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  18. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

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  19. The vectors vec(a) = - 4hat(i) + 3hat(k), vec(b)

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  20. Prove that : (vec(a) + vec(b)). { (vec(b)+vec(c))xx (vec(c)+vec(a))}...

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