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If vec a × vec b = vec b × vec c != 0, P...

If `vec a × vec b = vec b × vec c != 0`, Prove that `vec a + vec c = m vec b`, `m` is a scalar.

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MODERN PUBLICATION-VECTOR-EXERCISE
  1. Are three points with position vectors vec a + vec b, vec a - vec b an...

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  2. Find the unit vector perpendicular to i + j and i + k.

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  3. If vec a × vec b = vec b × vec c != 0, Prove that vec a + vec c = m ve...

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  4. Let vec a is any vector than what is the value of (vec a.hat i)hat i+(...

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  5. What is the value of (hat i+hat j)×(hat j+hat k).(hat k+hat i)?

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  6. If vec Avec C and vec Bvec D are the diagonals of the parallelogram AB...

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  7. Find the area of the parallelogram whose adjacent sides are gives by t...

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  8. If vec(a) and vec(b) are two vectors such that |vec(a) + vec(b)| = |ve...

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  9. Determine the area of parallelogram whose adjacent sides are the vecto...

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  10. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  11. Prove that (vec a × vec b).(vec c × vec d) = [[vec a.vec c,vec a.vec d...

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  12. Find a unit vector in direction of vec a-vec b, when vec a = 4 hat i +...

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  13. If vec a and vec b be perpendicular vectors, then prove that (vec a + ...

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  14. Find the value of lambda so that the three vectors are co-planar. (2,-...

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  15. Determine k such that a vector vec(r) is at right angles to each of th...

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  16. Find the scalar and vector projection of veca on vecb. veca = hati+hat...

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  17. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  18. Prove that : |veca + vecb|le|veca|+|vecb|.

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  19. Show that vec a × (vec b+vec c) + vec b × (vec c+vec a) + vec c × (vec...

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  20. If vec(a) and vec(b) are unit vectors, then what is the angle between ...

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