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If A,B,C,D are the points with position vectors : `hati+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk,3hati-2hatj+hatk` respectively, find the projection of `vec(AB)` along CD.

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If A,B,C,D are the points with positon vectors hat(i)+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk,3hati-2hatj+htk , respectively find the projection of vec(AB) along vec(CD) .

Show that the three points with position vectors hati+2hatj+7hatk , 2hati+6hatj+3hatk and 3hati+10hatj-hatk are collinear.

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk are the vertices of

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3hatj-5hatk,3hati-4hatj-4hatk .

Show that the points with position vectors veca=3hati-4hatj-4hatk,vecb=2hati-hatj+hatk and vecc=hati-3hatj-5hatk respectively form the vertices of a right angled triangle.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Dot product of a vector with vectors hati-hatj+hatk,2hatk+hatj+3hatk and hati+hatj+hatk are respectively 4,0 and 2. Find the vector.

The position vectors of A,B,C are 2hati+hatj-hatk,3hati-2hatj+hatk and hati+4hatj-3hatk respectively. Show that A, B and C are collinear.

MODERN PUBLICATION-VECTORS-Exercise
  1. If theta is the angle between two vectors veca and vecb, then |veca*ve...

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  2. Using vectors, find the value of 'k' such that the points (k,-10,3),(1...

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  3. If A,B,C,D are the points with position vectors : hati+hatj-hatk,2hati...

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  4. Parallelogram on equal bases and between the same parallels are equal ...

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  5. Write all the unit vectors in XY-plane.

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  6. Write down a unit vector in XY-plane, making an angle of 30^o with the...

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  7. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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  8. If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk, the...

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  9. If veca=2hati-hatj+hatk,vecb=hati+3hatj-hatk,vecc=-2hati+hatj-3hatk an...

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

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  11. The two adjacent sides of a parallelogram are given by the vectors 2ha...

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  12. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  13. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  14. If veca,vecb,vecc are three non-coplanar vectors and vecd*veca=vecd*ve...

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  15. If vecc is normal to veca and vecb, show that vecc is normal to veca+v...

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  16. Show that |veca|vecb + |vecb|veca is perpendicular to |veca|vecb-|vec...

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  17. Find the area of the parallelogram having diagonals veca+vecb and vecb...

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  18. Prove that the quadrilateral obtained by joining mid-points of adjacen...

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  19. Prove that 1/2 vec(AC)xxvec(BD) represents the vector area of the plan...

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  20. Given veca=1/7(2hati+3hatj+6hatk), vecb=1/7(3hati-6hatj+2hatk) , ve...

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