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Find the value of 'a' do the which the p...

Find the value of 'a' do the which the pointA,B,C with position vectors `2hati-hatj+hatk,hati-3hatj-5hatk` and `ahati-3hatj+hatk` respectively are the vertices of a right angled triangle with `/_C=pi/2`.

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Prove that the vectors 2hati-hatj+hatk , hati-3hatj-5hatk , 3hati-4hatj-4hatk are the sides of a right angled triangle.

If the points with position vectors 10hati+3hatj, 12hati-5hatj and ahati+11hatj are collinear, find the value of a.

Prove that four points with position vectors hati+hatj-3hatk, 2hati -hatj-hatk,- hati +2hatj +2hatk and 2hati +2hatk arecoplanar

Show that the vectors 4hati+4hatj+ 4hatk,7hati+6hatj-hatk and 3hati+2hatj-5hatk form a right angled triangle and find its area.

Find the value of lambda so that the three vectors are co-planar. hati+2hatj+3hatk, 4hati+hatj+lambdahatk and lambdahati-4hatj+hatk

Show that the vectors 2hati + 3hatj,5hati -5hatk and 6hatj + 4hatk are co-planar.

Find the unit vectors perpendicular to the vectors. 2hati-3hatj+hatk , -hati+2hatj-hatk .

Find the value of lambda so that three vectors veca=2hati-hatj+hatk, vecb=hati+2hatj-3 hatk and vecc= 3hati +lambda vecj+5 hatk are coplanar.

if veca=2hati-5hatj+8hatk, vecb=hati-3hatj-7hatk and vecc=-3hati+2hatj-hatk then find |veca+vecb+vecc|

Find the area of the parallelogram whose diagonals are vectors 3hati+hatj-2hatk and hati-3hatj+4hatk .

USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE
  1. Write the values of a and b, for which the vectors (a-1)hat(i) + (b+2)...

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  2. Find the value of 'a' do the which the pointA,B,C with position vector...

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  3. find the unit vector in the direction of 'PQ' where P and Q are the po...

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  4. If A, B, C and D are the vertices of a square, find vec(AB) + vec(BC)+...

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  5. If vec(OP1)=4hati+3hatj and vec(OP2)=8hati-5hatj find vec(p1p2)

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  6. If A, B, C and D are the vertices of a square, find vec(AB) + vec(BC)+...

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  7. Find the magnitude: 5/2 and is parallel to the vector 3hati+4hatj.

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  8. Find the vector from the origin O to the centroid of the triangle whos...

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  9. If G is centroid of the triangle ABC,then find vec(GA)+vec(GB)+vec(GC)...

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  10. Find veca*(vecaxxvecb).

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  11. Find veci*(veckxxvecj)

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  12. Find veci*(vecjxxveck)

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  13. find the position vector of the mid point of the vector joining the p...

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  14. Evaluate:hatixx(hatjxxhatk)+hatjxx(hatkxxhati)+hatkxx(hatixxhatj)

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  15. Using vector method find the area of the triangle with vertices (1, 0,...

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  16. What is the distance of the point (4, 5, -3) from y-axis ?

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  17. What is the distance of point (1,2,3,)from yz-plane?

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  18. What is the distance of the point (x, y, z) from x-axis?

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  19. Find the image of the point (5,3,-2)w.r.t yz-plane.

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  20. Find the number of points (x, y, z) in space other than the point (1,-...

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