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If a, b, c be three non-zero vectors, t...

If a, b, c be three non-zero vectors, then the equation a. b = a. c implies

A

b = c

B

a is orthogonal to both b and c

C

a is orthogonal to b-c

D

either a is orthogonal to both b and c or a is orthogonal to b -c

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The correct Answer is:
A, C
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
  1. Three points with position vectors, a, b, c are collinear if

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  2. theta is the angle between two vectors a and b then a. b le 0 only if

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  3. If a, b, c be three non-zero vectors, then the equation a. b = a. c ...

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

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

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

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

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

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

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

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

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

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

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

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

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  17. 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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  18. 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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  19. The angle between (vecA xx vec B) and (vecB xx vecA ) is :

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

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