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If vec(a)= -vec(i) + vec(j) + vec(k), ve...

If `vec(a)= -vec(i) + vec(j) + vec(k), vec(b)= vec(i)-vec(j) + vec(k), vec(c )= vec(i) + vec(j)-vec(k)`, then the vectors `vec(a) xx vec(b), vec(b) xx vec(c ), vec(c ) xx vec(a)` are

A

collinear

B

mutually perpendicular

C

linearly dependent

D

linearly independent

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Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Practice Exercise
  1. (vec(a) + vec(b)) xx (vec(a)-vec(b)) + (vec(b) + vec(c )) xx (vec(b)-v...

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  2. If vec(a)= -vec(i) + vec(j) + vec(k), vec(b)= vec(i)-vec(j) + vec(k), ...

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  3. Observe the following statements Assertion (A): (a-b) (vec(p) xx vec...

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  4. Let |vec(a) + vec(b)| = |vec(a)-vec(b)|. If |vec(a) xx vec(b)|= lamda ...

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  5. (vec(a) xx vec(b), vec(b) xx vec(a))=

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  6. Given vec(a) = vec(i) + vec(j)-vec(k), vec(b)= - vec(i) + 2vec(j) + ve...

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  7. Number of vectors of unit length perpendicular to the vectors vec(a)= ...

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  8. The unit vector perpendicular to vectors vec(i)-vec(j) and vec(i) + ve...

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  9. If vec(a)= 2vec(i) + vec(j)-3vec(k), vec(b)=vec(i) -2vec(j) + vec(k), ...

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  10. Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx...

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  11. If |vec(a)| = |vec(b)|=2, then (vec(a) xx vec(b))^(2) + (vec(a).vec(b)...

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  12. Which of the following statements are true. Statement-I: (vec(r ).ve...

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  13. If r. a = r.b = r.c = 0 where a,b,c are noncoplannar, then

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  14. A vector vec( c) perpendicular to the vectors 2vec(i) + 3vec(j)-vec(k)...

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  15. The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and ve...

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  16. If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0...

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  17. Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, ...

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  18. The area of the parallelogram is 4sqrt29 sq.u. If one of adjacent side...

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  19. ABCD is a quadrilateral with vec(AB)= vec(a), vec(AD)= vec(b) and vec(...

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  20. The perpendicular distance from A(1, 4, -2) to BC, where B= (2, 1, -2)...

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