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Find the angle between the following vec...

Find the angle between the following vectors :
(i) `veca = 2hati-6hatj+3hatk` and `vecb = hati+2hatj-2hatk`
(ii) `veca=6hati+3hatj-2hatk` and `vecb=4hati-2hatj+9hatk`

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The correct Answer is:
(i) `cos^(-1)(16/21)`, (ii) `90^(@)`
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NAGEEN PRAKASHAN-THREE-DIMENSIONAL GEOMETRY -Exercise 11 A
  1. Find the direction cosines of that line whose direction ratios are as ...

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  2. Find the direction cosines of the line joining the following points : ...

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  3. Show that the point A(2,-3,-4), B(1,2,3), C(3,-8,-11) are collinear.

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  4. Find the angle between those lines whose direction ratios are as foll...

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  5. Find the angle between the following vectors : (i) veca = 2hati-6ha...

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  6. Show that the joint of the points (1,2,3), (4,5,7) is parallel to the ...

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  7. If the co-ordinates of four points in space are A(6,-6,0), B(-1,-7,6),...

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  8. If vec r is a vector of magnitude 21 and has direction ratios 2,-3...

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  9. Find the angles which the following vectors, makes form the co-ordinat...

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  10. Find the angle between the lines whose direction cosines are given by ...

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  11. Prove that the lines whose directioncosines are given by the equtions ...

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  12. If the direction cosines of two lines are l(1), m(1), n(1) and l(2), m...

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  13. Find the angel between any two diagonals of a cube.

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  14. Find the angle between two lines whose direction ratios are proport...

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  15. Find the angles of a triangle whose verties are A(3,2,1), B(35,2) and ...

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  16. If a line makes angles 90o," "135o," "45o with the x, y and z-axes ...

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  17. Find the direction cosines of a line which makes equal angles with ...

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  18. If a line has the direction ratios 18 , 12 , 4, then what are its ...

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  19. Show that the points (2,3,4),(-1,-2,1),(5,8,7) are collinear.

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  20. Find the direction cosines of the sides of the triangle whose vertice...

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