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show that the direction of cosines of a ...

show that the direction of cosines of a vector equally inclined to the axes OX,OY and OZ are '1/3^1/2,1/3^1/2,1/3^1/2.

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USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE
  1. Prove the following by vector method. Median to the base of an isoscel...

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  2. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  3. show that the direction of cosines of a vector equally inclined to the...

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  4. If veca=vecb+vecc, then write the value of veca*(vecbxxvecc).

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  5. If D is the mid point of side BC of a triangleABC, show by vector meth...

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  6. Find the scalar components of a unit vector which is perpendicular to ...

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  7. Decompose the vector 6hati-3hatj-6hatk into vectors which are parallel...

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  8. Express 2hati-hatj+3hatk as the sum of a vector parallel, and a vector...

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  9. Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...

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  10. Find the angle between the following pair of the planes.2x+y+2z-4=0and...

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  11. Show that the join of the points (6,-4,4) and (0,0,-4) intersects the ...

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  12. Show that the points (2,3,-5) and (3,4,7) lie on the opposite side of ...

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  13. Find dy/dx if y=log(sec x+tan x).

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  14. Obtain the equation of the line through the point (1, 2, -3) and perpe...

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  15. Find the shortest distance between the lines frac[x][2]=frac[y][-3]=fr...

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  16. Find the equation of the plane passing through the line frac[x+1][-3]=...

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  17. Find the equation of the plane containing the line frac[x+3][3]=frac[y...

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  18. Show that lines vecr = (hat(i) + hat(j) - hat(k)) + lambda(3hat(i) - h...

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  19. If P is the point (2,1,6), then find the point Q such that PQ is perpe...

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  20. The plane lx+my=0 is rotated about its line of intersection with the p...

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