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If the direction cosines of two lines ar...

If the direction cosines of two lines are `l_(1), m_(1), n_(1)` and `l_(2), m_(2), n_(2)`, then find the direction cosine of a line perpendicular to these lines.

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The direction Cosines of two lines at right angles are l_(1),m_(1),n_(1)and l_(2),m_(2),n_(2) Then the direction cosines of a line which is perpendicular to both these lines are

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If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two lines and l , m, n are the direction cosines of a line perpendicular to the given two lines, then

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) The angle between the lines whose direction cosines are (1/2, 1/2,1/sqrt(2)) and (-1/2, -1/2, 1/sqrt(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If l_(1)=1/sqrt(3), m_(1)=1/sqrt(3) then the value of n_(1) is equal to

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

The direction cosines to two lines at right angles are (1,2,3) and (-2,1/2,1/3) then the direction cosine prependicular to both the given lines are

If l,m,n are direction cosines of the line then -l,-m,-n can be

If (l,m,n) are direction cosines of a line then L^(2)+m^(2)+n^(2)

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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