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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 - Direction Cosines and Direction Ratios of a Line

Question

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

Solution

Given direction ratios are:

2,1, 1 and 3, 4,1
Let a, b and c be the direction ratios of the line perpendicular to the given lines.
Thus, we have,
-2a + b - c = 0
-3a - 4b+c = 0
Cross multiplying, we get,

`a/(1xx1-(-4)xx(-1))=b/((-3)xx(-1)-(-2)xx1)=c/((-2)xx(-4)-(-3)xx1)` 

`a/(1-4)=b/(3+2)=c/(8+3)`

`a/-3=b/5=c/11`

Let us find `sqrt(a^2_b^2+c^2)`

`sqrt(a^2_b^2+c^2)=sqrt((-3)^2_5^2+11^2)`

                      = `sqrt(9+25+121)=sqrt(155)`

Thus, the direction ratios of the required line are  -3,5,11

The direction cosines are:  `-3/sqrt155,5/sqrt155,11/sqrt155`

Is there an error in this question or solution?

APPEARS IN

2014-2015 (March)
Question 2.2.1 | 4 marks
Solution for question: 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. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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