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If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are...

If `(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))` are d.c's of two lines then find the value of `(l_(1)m_(2)-l_(2)m_(1))^(2)+(m_(1)n_(2)-n_(1)m_(2))^(2)+(n_(1)l_(2)-n_(2)l_(1))^(2)+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^(2)`

A

3

B

2

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DIRECTION COSINES & RATIOS-PRACTICE EXERCISE
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  2. If the d.r's of bar(OA),bar(OB) are (1,-2,3),(-3,4,5) then the d.c's ...

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  3. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are d.c's of two lines then find ...

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  4. If the d.c's of the two lines are (2)/(3),(2)/(3),(1)/(3),(5)/(13),(12...

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  5. If (6,-2,-3),(1,2,2) are d.r's of two lines then the d.c's of line bis...

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  6. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are direction cosines of two line...

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  7. If the d.c's (l,m,n) of two lines are related as l + m + n = 0, 2lm -...

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  8. If the d.c's (l,m,n) of two lines are connected by the relations 3l+m+...

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  9. If the direction rations of two lines are given by 3lm-4ln+mn = 0 and ...

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  10. If the d.c's of two lines are such that l+3m+n = 0, 3l^(2) + 5m^(2) - ...

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  11. If the d.c's (l,m,n) of two lines are connected by the relations 7l^(...

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  12. The angle between two lines whose d.c's satisfy the equation n = l + m...

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  13. Assertion (A): The points A(2,3,5) B(4,6,10), C(8,12,20) are collinear...

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  14. The projection of a vector on the three coordinate axes are 6,-3,2 res...

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  15. The projection of the join of the points (3,4,2), (5,1,8) on the line ...

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  16. The projection of the join of the two points (1,4,5), (6,7,2) on the l...

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  17. A (x(1),y(1),z(1)), B(x(2),y(2),z(2)) are two points. Then the lenghts...

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  18. If A(1,2,3), B(6,7,7), C(9,9,0) are three points, then the foot of the...

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  19. Assertion (A): A(x(1),y(1),z(1)), B(x(2),y(2),z(2)). The projection of...

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  20. A line makes the same angle theta, with each of the x and z axis. If t...

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