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Find the Direction Cosines of the Line Perpendicular to the Lines Whose Direction Ratios Are -2, 1,-1 and -3, - 4, 1 - Mathematics and Statistics

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Question

Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1 

Solution

Let `bara   "and"   barb` be the vectors along the lines whose direction ratios are -2, 1, -1 and -3, -4, 1 respectively.

∴ `bara = -2hati + hatj - hatk and hatb = -3hati - 4hatj + hatk`

A vector perpendicular to both `bara and barb` is given by

`bara xx barb = |(hati, hatj, hatk), (-2, 1, -1), (-3, -4, 1)|`

= `( 1 - 4 )hati - ( - 2 - 3 )hatj + ( 8 + 3 )hatk`

= `-3hati + 5hatj + 11hatk`

∴ the direction ratios of the required line are -3, 5, 11
Now, `sqrt( 9 + 25 + 12)  = sqrt155`

Direction cosine of the line are `-3/sqrt155, 5/sqrt155, 11/sqrt155`.

  Is there an error in this question or solution?
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APPEARS IN

 2014-2015 (March) (with solutions)
Question 2.2.1 | 4.00 marks
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Solution Find the Direction Cosines of the Line Perpendicular to the Lines Whose Direction Ratios Are -2, 1,-1 and -3, - 4, 1 Concept: Direction Cosines and Direction Ratios of a Line.
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