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Prove that the following vectors are ...

Prove that the following vectors are non-coplanar: `3 hat i+ hat j- hat k ,2 hat i- hat j+7 hat k` and `7 hat i- hat j+23 hat k` ` hat i+2 hat j+3 hat k ,2 hat i+ hat j+3` and ` hat i+ hat j+ hat k`

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Prove that the following vectors are non coplanar: 3 hat i+ hat j- hat k ,2\ hat i- hat j+7 hat k\ a n d\ 7 hat i- hat j+23 hat k

Prove that the following vectors are non-coplanar: hat i+2 hat j+3 hat k ,2\ hat i+ hat j+3 hat k\ a n d\ hat i+ hat j+ hat k

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k

Show that the points whose position vectors are as given below are collinear: 2 hat i+ hat j- hat k ,\ 3 hat i-2 hat j+ hat k\ a n d\ hat i+4 hat j-3 hat k 3 hat i-2 hat j+4 hat k ,\ hat i+ hat j+ hat k\ a n d-\ hat i+4 hat j-2 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Evaluate : [ hat i hat j hat k]+[ hat j hat k hat i]+[ hat k hat i hat j] [2 hat i hat j hat k]+[ hat i hat k hat j]+[ hat k hat j2 hat i]

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Prove that a necessary and sufficient condition for three vectors ...

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  2. Prove that the following vectors are non-coplanar: 3 hat i+ hat j- ...

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  3. Using vectors show that the points A(-2,3,5), B(7,0,-1), C(-3,-2,-5) a...

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  4. Prove that 1,1,1 cannot be direction cosines of a straight line.

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  5. A vector vec r is inclined at equal acute angles of x-axis , y-axi ...

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  6. Find the angles at which the following vectors are inclined to each...

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  7. Find the direction cosines of the following vectors: 2 hat i+2 hat...

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  8. Prove that the sum of three vectors determined by the medians of a ...

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  9. If P is a point and A B C D is a quadrilateral and vec A P+ vec...

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  10. If vec a is a vector and m is a scalar such that m vec a= vec0 ...

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  11. If vec a , vec b are two vectors, then write the truth value of th...

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  12. A B C D is a quadrilateral. Find the sum the vectors vec B A , ve...

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  13. A B C D E is pentagon, prove that vec A B + vec B C + vec C D ...

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  14. If P ,Q and R are three collinear points such that vec P Q= vec a ...

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  15. Give a condition that three vectors vec a , vec b and vec c from ...

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  16. If vec a and vec b are two non-collinear vectors having the same ...

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  17. Find the unit vector in the direction of 3 hat i+4 hat j-12 hat kdo...

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  18. The vertices A , B , C of triangle A B C have respectively position ...

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  19. Find a unit vector parallel to the vector hat i+sqrt(3) hat j

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  20. Show that the four points A ,B ,C ,D with position vectors vec a , ve...

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