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Show that the vectors 2 hat i -3 hat j +...

Show that the vectors `2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k` are collinear.

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Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

Find p if the vectors 2 hat i +3 hat j + 6 hat k and p hat i+2 hat j-3 hat k are perpendicular.

Find the angle between the vectors 3 hat i-2 hat j -6 hat k and 4 hat i-hat j-8 hat k .

Find a vector of magnitude 6 units which is at right angles to both the vectors 2 hat i- hat j +2 hat k and 4 hat i- hat j+3 hat k

Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 hat i +22 hat j- 2 hat k and vec c = 2hat i -8 hat j +16hat k are coplanar.

Find a unit vector perpendicular to both the vectors (3 hat i + 2 hat j - hat k) and ( hat i + 2 hat j + hat k) .

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

Find a unit vector perpendicular to both the vectors 4 hat i-hat j+3 hat k and -2 hat i+hat j-2 hat k .

Find the sine of the angle between the vectors : 2 hat i+ 4 hat j+ 4 hat k and 2 hat i- 7 hat j+ hat k .

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. For given vectors, vec a =2 hat i- hat j+2hat k and vec b =-hat i +hat...

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  2. Find a vector in the direction of vector 5veci - vecj + 2veck which ha...

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  3. Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j ...

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  4. Find the direction cosines of the vector hat i + 2 hat j+ 3 hat k.

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  5. Find the direction cosines of the vector joining the points A(1,2,-3) ...

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  6. Show that the vector veci+vecj+veck is equally inclined to the axes O...

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

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

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  9. Find the position vector of the mid-point of the vector joining the po...

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  10. Show that the points A, B and C with position vectors, vec a= 3hat i-4...

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  11. If vec a and vec b are two collinear vectors then which of the followi...

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  12. Find the angle between two vectors veca and vecb with magnitudes sqrt3...

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  13. Find the angle between the vectors hat i -2 hatj +3 hat k and 3 hat i ...

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  14. Find the projection of the vector hat i - hat j on the vector hat i +...

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  15. Find the projection of the vector hat i +3 hat j +7 hatk on the vector...

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  16. Show that each of the given three vectors is a unit vector : 1/7 (2 ha...

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  17. Find |vec a| and |vec b| lf(veca + vec b)*(vec a-vec b)=8 and |vec a |...

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  18. Evaluate the product (3 vec a-5 vec b)*(2 vec a+7 vec b).

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  19. Find the magnitude of two vectors veca and vecb, having the same magni...

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  20. If vec a =2 hat i + 2 hat j +3 hat k, vec b=-hat i + 2 hat j +hat k t...

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