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Prove that four points with position vec...

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

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

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

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

If veca = hati+2hatj-hatk , vecb = hati+hatj+2hatk , vecc = 2hati-hatj then

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

If veca = hati+2hatj+hatk , vecb = 2hati- 2hatj + 2hatk and vecc = hati + 2hatj + hatk then

Find the unit vector in the direction of 6hati +2hatj +3hatk .

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+4hatj+5hatk, -2hati+4hatj-4hatk .

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

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  2. Find the value of lambda such that the following vectors are coplanar:...

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  3. Prove that four points with position vectors hati+hatj-3hatk, 2hati -h...

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

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  5. Write the volume of the parallelopiped whose sides are given by-hatj, ...

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  6. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  7. Write a vector normal to hati+hatk and hati+hatj.

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  8. If vec a = (2,-2,1), vec b = (2,3,6) and vec c = (-1,0,2),Find the mag...

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  9. Find the angle between the vectors 3hati+ 4hatj and2hati+hatj+hatk.

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  10. Find the unit vector in the direction of veca-vecb where veca= 4hati +...

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  11. If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-v...

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  12. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

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  13. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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  14. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

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  15. Show that veca, vecb and vec c are coplanarif veca+vecb,vecb+vecc and ...

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  16. Find the vector vecp which is perpendicular to both vecalpha = 4hati +...

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  17. If veca=hati+hatj+hatk and vecb=hati-hatk . Find a vector vecc such th...

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  18. If veca,vecb and vecc are three vectors such that |veca|=5,|vecb|=12,|...

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  19. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  20. Prove the following by vector method. in any triangle ABC, a = bcosC...

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