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Find the sum of the vectors vec a= hat i...

Find the sum of the vectors `vec a= hat i-2 hatj + hat k, vec b= -2 hat i + 4 hatj +5hat k` and `vec c =hat i-6 hat j-7 hat k`,

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Find a unit vector parallel to the sum of the vector vec a= hat i+ hat j+ hat k , vec b= 3 hat i+ hat j- 4 hat k and vec c=-2 hat i- hat j-hat k .

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = -3hat i+7 hat j + 5 hat k, vec b=-5 hat i +7 hat j- 3 hat k and vec c = 7 hat i -5 hat j -3 hat k .

Show that the points A, B and C with position vectors, vec a= 3hat i-4 hatj -4 hat k, vec b= 2 hat i -hatj +hat k and vec c =hat i-3hat j-5 hat k , respectively, form the vertices of a right angled triangle.

Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 hat i -hat j - hat k and vec c= λ hat i +7 hat j +3 hat k are coplanar.

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 the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = 2 hat i- 3 hat j + 4 hat k, vec b= hat i +2 hat j- hat k and vec c = 3 hat i -hat j +2 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.

Prove that the vectors vec a = hat i- 2 hat j+ hat k , vec b= -2 hat i+ hat j+ hat k and vec c= hat i+ hat j-2 hat k are coplanar.

Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + 3hat j- 4hat k and vec c =hat i - 3 hat j+5 hat k are coplanar.

Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the values of x and y so that the vectors 2 hat i +3 hat j and x...

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  2. Find the scalar and vector components of the vector with initial point...

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  3. Find the sum of the vectors vec a= hat i-2 hatj + hat k, vec b= -2 hat...

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  4. Find the unit vector in the direction of the vector vec a= hat i+ hatj...

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  5. Find the unit vector in the direction of vector vec(PQ), where P and Q...

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  6. For given vectors, vec a =2 hat i- hat j+2hat k and vec b =-hat i +hat...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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