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Show that the vector overset^^i+overset^...

Show that the vector `overset^^i+overset^^j+overset^^k` is equally inclined to the axes OX,OY and OZ.

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Show that the direction cosines of a vector equally inclined to the axes O X, OY and O Z are 1/(sqrt3), 1/(sqrt3), 1/(sqrt3)

Show that the vectors 2overset^^i-overset^^j+overset^^k, overset^^i-3overset^^j-5overset^^k and 3overset^^i-4overset^^j-4overset^^k form the vertices of a right angled trainagle.

Find the values of x and y so that the vectors 2overset^^i+3overset^^j "and" xoverset^^i+yoverset^^j are equal.

The scalar product of the vector overset^^i+overset^^j+overset^^k with a unit vector along the sum of the vectors 2overset^^i+4overset^^j-5overset^^k"and" lambdaoverset^^i+2overset^^j+3overset^^k is equal to I.Find the value of lambda .

Compute the magnitude of oversetrarra =overset^^i+overset^^j+overset^^k ,vector

Find the value of x for which x(overset^^i+overset^^j+overset^^k) is a unit vector.

Show that the vectors 2overset^^i-3overset^^j+4overset^^k"and " -4overset^^i+6overset^^j-8overset^^k are collinear.

Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2overset^^i+3overset^^j-4overset^^k and vecc=overset^i-3overset^j+5overset^^k are coplanar.

Compute the magnitude of oversetrarrb=2overset^^i-7overset^^j-3overset^^k ,vector

Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^i+overset^^j+2overset^^k " and " overset^^i+lambdaoverset^^j-3overset^^k are coplanar.

V PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Find the direction cosines of the vector hati+2 hatj+3 hatk

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  2. Find the, direction cosines of the vector joining 'A(1,2,-3)' and 'B(-...

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  3. Show that the vector overset^^i+overset^^j+overset^^k is equally incli...

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  4. Find the position vector of a point R which divides the line joining t...

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  5. Find the position vector of the mid point of the vector joining the po...

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  6. Show that the points A, B and C with position vectors veca=3i-4j-4k,ve...

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  7. In triangle 'ABC', which of the following is not true. (##VPUHSSMATX...

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  8. If oversetrarra"and"oversetrarrbare two collinear vectors, then which ...

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  9. Find the angle between two vectors veca and vecb with magnitudes 1 and...

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  10. Find the angle between the vectors veca=hati+hatj-hatk and vecb=hati-h...

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  11. If veca=5i-j-3k and vecb=i+3j+5k,then show that the vectors veca+vecb,...

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  12. Find the projection of the vector veca=2 hati+3 hatj+2 hatk on the vec...

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  13. Find |veca-vecb|, if two vectors veca and vecb are such that |veca|=2,...

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  14. If veca is a unit vector and (vecx-veca) .(vecx+veca)=8, then find |ve...

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  15. For any two vectors veca and vecb, we always have |veca+vecb| le|veca|...

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  16. Show that the points A(-2 hati+3 hatj+5 hatk), B(hati+2 hatj+3 hatk) a...

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  17. Find the angle between two vectorsoversetrarra"and"oversetrarrb with m...

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  18. Find the angle between the vectors hati-2 hatj+3 hatk and 3 hati-2 hat...

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  19. Find the projection of the vector hati-hatj on the vector hati+hatj.

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  20. Find the projection of a vector i+3j+7k on the vector 7i-j+8k.

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