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If vec(a) and vec(b) are two vectors suc...

If `vec(a) and vec(b)` are two vectors such that `vec(a).vec(b) = 0 and vec(a) xx vec(b) = 0`, then which one of the following is correct?

A

a is parallel to b

B

a is perpendicular to b

C

either `a = 0 or b = 0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
  1. If a, b, c be three non-zero vectors, then the equation a. b = a. c ...

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  2. If a. b = a . C and axx b = a xx c, then

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  3. If vec(a) and vec(b) are two vectors such that vec(a).vec(b) = 0 and v...

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  4. If a xx b = c and b xx c = a , then

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  5. If a.b = b.c = c.a = 0, then a.(bxxc)=

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  6. If p = a xx (b + c) + b xx (c + a) + c xx (a + b) q = a xx (b xx c) ...

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  7. If a and b are not perpendicular to each other and r xx a = b xx a, r....

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  8. Let the vectors vec(PQ),vec(QR),vec(RS), vec(ST), vec(TU) and vec(UP) ...

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  9. If r satisfies the equation r xx (i+2j+k) = i-k then for any scalar la...

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  10. If a = 2i+j+k, b =i+2j+k,c=2i-3j+4k and r is a vector such that r xx b...

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  11. Given three vectors a,b,c such that b.c = 3 a.c = (1)/(3). The vector ...

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  12. Let vec r xx veca = vec b xx veca and vecc vecr=0, where veca.vecc ne ...

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  13. If a xx b = c xx d and a xx c = b xxd, then

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  14. If a and b include an angle of 120^(@) and their magnitudes are 2 and ...

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  15. u = q-r, r-p, p-q and v = (1)/(a),(1)/(b),(1)/(c). If a,b, c be T(p)...

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  16. In a G.P. T(p) = a, T(q) = b and T(r) = c where a, b, c are +ive then...

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  17. The angle between (vecA xx vec B) and (vecB xx vecA ) is :

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  18. The angle between the vectors 2i+3j+k and 2i-j-k is

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  19. If theta is the angle between vectors a and b, then |a xx b| = | a.b|,...

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  20. If |a|=2, |b|=5 and |a xx b|=8, then what is a, b equal to ?

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