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If ` vec a , vec b` are two non-collinear vectors, prove that the points with position vectors ` vec a+ vec b , vec a- vec b` and ` vec a+lambda vec b` are collinear for all real values of `lambdadot`

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Prove that the points having position vectors hat i+2 hat j+3 hat k ,...

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  2. If the points with position vectors 10 hat i+3 hat j ,12 hat i-5 ha...

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  3. If vec a , vec b are two non-collinear vectors, prove that the poi...

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  4. If vec A O+ vec O B= vec B O+ vec O C , prove that A , B , C are coll...

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  5. If the points A(m ,-1),\ B(2,1)a n d\ C(4,5) are collinear find the va...

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  6. Show that the vectors 2 hat i-3 hat j+4 hat k\ a n d-4 hat i+6 hat j-8...

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  7. Show that the points (3,4), (-5, 16), (5,1) are collinear.

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  8. If the vectors vec a=2 hat i-3 hat j\ a n d\ vec b=-6 hat i+m hat j ...

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  9. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

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

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  11. Show that the points whose position vectors are as given below are ...

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  12. Using vector method, prove that the following points are collinear: A...

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  13. Using vector method, prove that the following points are collinear: A...

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  14. Using vector method, prove that the following points are collinear: A...

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  15. Using vector method, prove that the following points are collinear: ...

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  16. If a ,\ b ,\ c are non zero non coplanar vectors, prove that the follo...

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

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

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

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

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