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Show that the point A ,B ,C with posi...

Show that the point `A ,B ,C` with position vectors ` vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c` and `-7 vec b+10 vec c` are collinear.

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Show that the point A,B,C with position vectors vec a-2vec b+3vec c,2vec a+3vec b-4vec c and -7vec b+10vec c are collinear.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b+2vec c and -8vec a+13vec b are collinear whatever be vec a,vec b,vec c .

Show that the points A,B,C with position vectors 2vec a+3vec b+5vec c,vec a+2vec b+3vec c and 7vec a-vec c respectively,are collinear.

The points with position vectors vec a-2vec b+3vec c,2vec a+lambdavec b-4vec c,-7vec b+10vec c will be collinear if lambda=...cdots

Show that the points whose position vectors are vec(a) + 2vec(b) + 5vec(c), 3vec(a) + 2vec(b) + vec(c), 2vec(a) + 2vec(b) + 3vec(c) are colliner.

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

vec a * {(vec b + vec c) xx (vec a + 2vec b + 3vec c)} = [vec with bvec c]

Show that the found points A,B,C,D with position vectors vec a,vec b,vec c,vec d respectively such that 3vec a-2vec b+5vec c-6vec d=vec 0 ,are coplanar .Also,find the position vector of the point of intersection of the line segments AC and BD.

If the position vectors of three points are vec a-2vec b+3vec c,2vec a+3vec b-4vec c,-7vec b+10vec c then the three points are

MOTION-VECTOR -EXERCISE - 3
  1. The position vector of two points A and B are 6vec(a) + 2vec(b) and ...

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  2. In a triangleOAB, E is the mid-point of BO and D is a point on AB such...

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  3. Show that the point A ,B ,C with position vectors vec a-2 vec b...

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  4. If vec(r) = (hat(i) + 2hat(j) + 3hat(k)) + lambda(hat(i) - hat(j) + ha...

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  5. If the three successive vertices of a parallelogram have the position ...

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  6. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

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  7. If the three successive vertices of a parallelogram have the position ...

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  8. If hat(e(1)) and hat(e(2)) are two unit vectors such that vec(e(1))...

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  9. For any two vectors veca and vecb, prove that ((veca )/(|vec a |^2)-...

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  10. Given that vecx + 1/(vecp)^2 (vecp . vecx) vecp = vecq , show that vec...

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  11. .Find out whether the following pairs of lines are parallel, non-paral...

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  12. Find out whether the following pairs of lines are parallel, non parall...

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  13. Find out whether the following pairs of lines are parallel, non parall...

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  14. Let O A C B be a parallelogram with O at the origin andO C a diagonal....

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  15. Find the shortest distance between the lines : vec(r) = (4hat(i) - ha...

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  16. Let vec(A) = 2hat(i) + hat(k), vec(B) = hat(i) + hat(j) + hat(k) and ...

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  17. Find vector vec(v) which is coplanar with the vectors hat(i) + hat(j...

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  18. Find the point R in which the line AB cuts the plane CDE, where positi...

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  19. The position vectors of the angular points of a tetrahedron are A(3 ha...

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  20. Show that the four points with position vectors4 hat i+8 hat j+12 hat ...

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