HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Solution for Find the Direction Cosines of the Line Perpendicular to the Lines Whose Direction Ratios Are -2, 1,-1 and -3, - 4, 1 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptDirection 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

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 2.2.1 | 4.00 marks
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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