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Find the direction cosines of the unit v...

Find the direction cosines of the unit vector perpendicular to the plane`vecr.(2hati+3hatj-6hatk)-21=0`, through the origin.

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USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE
  1. If P (1,y,z) lies on the line through (3,2,-1) and (-4,6,3) find y & z...

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  2. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  3. Find the direction cosines of the unit vector perpendicular to the pla...

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  4. Find the equation of the plane through the points (1,0,-1),(3,2,-2)and...

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  5. A variable plane passes through a fixed point (a,b,c) and meets the co...

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  6. Find the equation plane passing through the point (2,3,1 )and perpendi...

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  7. Find the equation of the plane passing through the line x = y = z and ...

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  8. Prove the following by vector method. Median to the base of an isoscel...

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

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

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

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

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

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

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

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

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

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

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

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

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