HSC Science (General) 12th Board ExamMaharashtra State Board
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A line makes angles of measures 45° and 60° with positive direction of y and z axes respectively. Find the d.c.s. of the line and also find the vector of magnitude 5 along the direction of line. - HSC Science (General) 12th Board Exam - Mathematics and Statistics

ConceptLine Equation of Line Passing Through Given Point and Parallel to Given Vector

Question

A line makes angles of measures 45° and 60° with positive direction of y and z axes respectively. Find the d.c.s. of the line and also find the vector of  magnitude 5 along the direction of line.

Solution

Let α, β, γ be the direction angles of the line

β=45°, γ=60°

m=cosbeta=cos45^@=1/sqrt2 and n=cos gamma=cos 60^@=1/2

Since, cos^2alpha+cos^2beta+cos^2gamma=1

therefore cos^2alpha+(1/sqrt(2))^2+(1/2)^2=1

therefore cos^2alpha=1-1/2-1/4=1/4

therefore cos alpha=+-1/2

i.e l=+-1/2,m=1/sqrt2,n=1/2

The unit vectors along the direction of line are

hatu=lhati+mhatj+nhatk

=+-1/2hati+1/sqrt2hatj+1/2hatk

∴ The vectors of magnitude 5 are

5(1/2hati+1/sqrt2hatj+1/2hatk) and 5(-1/2hati+1/sqrt2hatj+1/2hatk)

Is there an error in this question or solution?

APPEARS IN

2015-2016 (July) (with solutions)
Question 2.2.2 | 4.00 marks

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Solution A line makes angles of measures 45° and 60° with positive direction of y and z axes respectively. Find the d.c.s. of the line and also find the vector of magnitude 5 along the direction of line. Concept: Line - Equation of Line Passing Through Given Point and Parallel to Given Vector.
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