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Show that the four points having posi...

Show that the four points having position vectors `6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k` are coplanar.

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Show that the points having position vectors 6 hat i-7 hat j ,\ 16 hat i-19 hat j-4 hat k ,\ 3 hat j-6 hat k ,\ 2 hat i+5 hat j+10 hat k are not coplanar.

Show that four points whose position vectors are 6 hat i-7 hat j ,\ 16 i-19 hat j-4 hat k ,\ 3 hat i-6 hat k ,\ 2 hat i-5 hat j+10\ hat k are coplanar.

The four points whose position vector are 6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat j - 6 hat k, 2 hat i + 5 hat j + 10 hat k are coplanar

Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k and 2 hat i+5 hat j+10 hatk form a tetrahedron in space.

Find the value of lambda for which the four points with position vectors - hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k and 4 hat i+4 hat j+4 hat k are coplanar.

Find the value of lambda for which the four points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and4 hat i+5 hat j+lambda hat k are coplanar.

Prove that the points having position vectors hat i+2 hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k ,\ -3 hat i-2 hat j-5 hat k are collinear.

Show that the four points with position vectors 4 hat i+8 hat j+12 hat k ,\ 2 hat i+4\ hat j+6 hat k ,3 hat i+5\ hat j+4 hat k\ a n d\ 5 hat i+8\ hat j+5 hat k are coplanar.

Show that the four points A, B, C and D with position vectors 4 hat i+5\ hat j+ hat k ,-(\ hat j+ hat k),3 hat j+9\ hat j+4 hat k\ a n d\ 4( hat i+ hat j+ hat k) , respectively are coplanar.

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If a ,\ b ,\ c are non zero non coplanar vectors, prove that the follo...

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  2. Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prov...

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  3. Show that the four points having position vectors 6 hat i-7 hat j ,...

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  4. Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,...

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  5. Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\...

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

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

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  8. If vec a ,\ vec b ,\ vec c are non coplanar vectors, prove that the...

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  9. If vec a ,\ vec b ,\ vec c are non coplanar vectors, prove that the...

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  10. Prove that a necessary and sufficient condition for three vectors ...

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  11. Show that the four points A ,B , Ca n dD with position vectors ...

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  12. The direction cosines of a vector vecr, which is equally inclined to O...

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  13. Can a vector have direction angles 45^0,60^0,120^0

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

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  15. A vector makes an angle of pi/4 with each of x-a xi s and y-a xi sd...

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

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  17. A vector vec r\ is inclined to x-axis at 45^0 and y-axis at 60^0dot ...

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

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

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

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