मराठी

If L1, M1, N1 And L2, M2, N2 Are the Direction Cosines of Two Mutually Perpendicular Lines, Show that the Direction Cosines of the Line Perpendicular to Both of These Are M1n2 − M2n1, N1l2 − N2l1, L1m2 ­− L2m1.

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प्रश्न

If l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1n1l2 − n2l1l1m2 ­− l2m1.

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उत्तर

It is given that l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines. Therefore,

Let lmn be the direction cosines of the line which is perpendicular to the line with direction cosines l1m1n1 and l2m2n2

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पाठ 11: Three Dimensional Geometry - Exercise 11.4 [पृष्ठ ४९७]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 11 Three Dimensional Geometry
Exercise 11.4 | Q 2 | पृष्ठ ४९७

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संबंधित प्रश्‍न

Which of the following represents direction cosines of the line :

(a)`0,1/sqrt2,1/2`

(b)`0,-sqrt3/2,1/sqrt2`

(c)`0,sqrt3/2,1/2`

(d)`1/2,1/2,1/2`


Write the direction ratios of the following line :

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If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.

(A) `0,1/sqrt2,-1/sqrt2`

(B) `0,-1/sqrt2,-1/sqrt2`

(C) `1,1/sqrt2,1/sqrt2`

(D) `0,-1/sqrt2,1/sqrt2`


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