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)`
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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.
