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Let l(1),m(1),n(1),l(2),m(2),n(2) and l(...

Let `l_(1),m_(1),n_(1),l_(2),m_(2),n_(2)` and `l_(3),m_(3), n_(3)` are direction cosine of three mutually perpendicular line OA, OB and OC. If the direction cosines of OP are proportional to `l_(1)+l_(2)+l_(3), m_(1)+m_(2)+m_(3), n_(1)+n_(2)+n_(3)` and angle made by OP with lines OA, OB, OC are respectively `theta_(1), theta_(2), theta_(3)`, then

A

`theta_(1) lt theta_(2) lt theta_(3)`

B

`theta_(1)=theta_(2)=theta_(3)`

C

`theta_(1) gt theta_(2) gt theta_(3)`

D

`theta_(1)=theta_(2)+theta_(3)`

Text Solution

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The correct Answer is:
B
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NIKITA PUBLICATION-THREE DIMENSIONAL GEOMETRY -MULTIPLE CHOICE QUESTIONS
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  2. The angle between diagonal of a cube and diagonal of a face of the c...

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  3. Let l(1),m(1),n(1),l(2),m(2),n(2) and l(3),m(3), n(3) are direction co...

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  4. The direction cosines of a line equally inclined to three mutually per...

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  5. Find the direction cosines of the two lines which are connected by ...

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

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  7. The direction ratios of vector perpendicular to the two lines whose di...

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  8. The direction ratios of a vector perpendicular to the two lines whose ...

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  9. Find the direction cosines of the line which is perpendicular to the l...

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  10. Direction ratios of the line which is perpendicular to the lines with ...

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  11. The direction cosines of the line which is perpendicular to the lines ...

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  12. The direction ratios of a line which is perpendicular to the two line...

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  13. The direction ratios of a line which is perpendicular to the two line...

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  14. Points (-2, 4, 7), (3, -6 -8) and (1, -2, -2) are

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  15. If the points (-1, 3, 3), (-2, 0, 1), (-4, -6, -3) and (2, 12, 9) are

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  16. prove that point A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, ...

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  17. The points (5, -4, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the v...

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  18. The points (5, 0, 2), (2, -6, 0), (4, -9, 6) and (7, -3, 8) are the ve...

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  19. The points (0, 7, 10), (-1, 6, 6), (-4, 9, 6) form

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  20. If the points A(4, 7, 6), B(2, 3, 2), C(-1, -2, -1) and D form a paral...

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