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

If `vec(a)=2hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)+3hat(j)+6hat(k) " and " vec(c)=-hat(i)+2hat(k)`, then find the magnitude and direction of the vector `vec(a)-vec(b)+2vec(c)`.

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The correct Answer is:
`sqrt(30)`, direction makes an angle `cos^(-1)(-2/sqrt(30))` with the positive direction of x-axis.
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CHHAYA PUBLICATION-VECTOR-EXERCISE - LONG ANSWER TYPE QUESTIONS
  1. If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " ...

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  2. By vector method, show that the four points (7, 2, -3), (6, 1, 4), (-3...

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  3. Find a unit vector in direction parallel to the sum of the vectors vec...

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  4. If vec(a)=2hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)+3hat(j)+6hat(k) " and...

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  5. The vectors vec(a) " and " vec(b) are non-collinear. Find for what val...

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  6. Given that the points with position vectors 12hat(i)-5hat(j), 10hat(i)...

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  7. The vectors vec(a) " and " vec(b) are non-collinear. If vec(p)=(x+4y)v...

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  8. If the sum of two unit vectors is a unit vector, prove that the magnit...

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  9. ABCDEF is a regular hexagon. If vec(CD)=vec(a), vec(DE)=vec(b), " find...

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  10. bar(AC) " and " bar(BD) are the diagonals of the parallelogram ABCD. P...

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  11. By vector method show that the figure formed by joining the mid-points...

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  12. Defination : Unit vector

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  13. ABCD is a parallelogram and P is the midpoint of the side bar(BC). Pro...

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  14. ABCD is a parallelogram, P and Q are the mid-points of the sides bar(A...

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  15. ABCD is a parallelogram and P is the mid-point of bar(DC). If Q is a p...

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  16. D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB...

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  17. C is the midpoint of the line segment bar(AB) and O is any point outsi...

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  18. G is a point inside the plane of the triangle ABC, if vec(GA)+vec(GB)+...

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  19. The diagonals of the parallelogram ABCD intersect at E. If vec(a), vec...

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  20. By vector method prove that the straight line joining the midpoints of...

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