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Show that the vectors `vec(a),vec(b)` and `vec(c )` are coplanar, if `vec(a)+vec(b),vec(b)+vec(c )` and `vec(c )+vec(a)` are coplanar.

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Hence, `vec(a),vec(b)` and `vec(c )` are coplanar.
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Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + vec(b) vec(b) + vec(c) vec(c) + vec(a)] = 2 [vec(a)vec(b)vec(c)]

For any three vectors vec(a), vec(b) and vec(c) , prove that vec(a) xx (vec(b) - vec(c)) = (vec(a) xx vec(b)) - (vec(a) xx vec(c)) .

For any three vectors vec(a), vec(b) and vec(c) , evaluate vec(a) xx (vec(b) + vec(c)) + vec(b) xx (vec(c) + vec(a)) + vec(c) xx (vec(a) + vec(b)) .

Prove that the four points with position vectors 2vec(a) + 3vec(b) - vec(c), vec(a) - 2vec(b) + 3vec(c) " , "3vec(a) + 4vec(b) - 2vec(c) and vec(a) - 6vec(b) + 6vec(c) are coplanar.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .

ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (1 MARK QUESTIONS)
  1. If vec(a)xxvec(b)=vec(b)xxvec(c )!=vec(0), then prove that vec(a)+ve...

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  2. What is the angle between the vectors 2hat(i) - hat(j) - hat(k) and ha...

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  3. Determine the area of the parallelogram whose sides are the vectors 2h...

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  4. Using vector method find the area of the triangle with vertices (1, 0,...

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  5. Write the angle between vec(a) and vec(c ), if vec(a)xx(vec(b)xxvec(c ...

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  6. What is (hat(i)-hat(j))*(hat(j)-hat(i)) ?

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  7. (2hat(i)-4hat(j))*(hat(i)+hat(j)+hat(k))= . . . .

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

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  9. Each question given below have four possible answers, out of which onl...

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  10. Each question given below have four possible answers, out of which onl...

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  11. Each question given below have four possible answers, out of which onl...

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  12. (-vec(a))*vec(b)xx(-vec(c))= . . . .

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  13. For the non-zero vectors vec(a),vec(b) and vec(c ),vec(a)*(vec(b)xxvec...

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  14. What is the projection of hat i + hat j - hat k upon the vector hat i ...

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  15. If hat(a) is a unit vector and (vec(x) - hat(a)).(vec(x) + hat(a)) = 8...

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  16. If |vec(a)|=sqrt(3),|vec(b)|=2 and vec(a)*vec(b)=3, then find the angl...

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  17. Find the angle between the vectors vec(a) and vec(b), if |vec(a)xxvec(...

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  18. Find vec(a).(vec(b) xx vec(c)), if vec(a) = 2hat(i) + hat(j) + 3hat(k)...

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  19. Show that the vectors vec(a),vec(b) and vec(c ) are coplanar, if vec(a...

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  20. Evaluate [hat(i) hat(k) hat(j)] + [hat(i) hat(j)hat(k)].

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