1.

If the direction cosines of the line are \(\frac{1}{2},-\frac{\sqrt{3}}{2}\),x respectively, then find the value of x.(a) 1(b) 0(c) \(\frac{\sqrt{3}}{2}\)(d) \(\frac{1}{2}\)The question was asked in a national level competition.My doubt stems from Direction Cosines and Direction Ratios of a Line in portion Three Dimensional Geometry of Mathematics – Class 12

Answer»

Correct answer is (B) 0

The EXPLANATION is: If the direction cosines of a line are l,m,n RESPECTIVELY, then

l^2+m^2+n^2=1

∴\(\FRAC{1}{2}^2+(\frac{\sqrt{3}}{2})^2+x^2=1\)

x^2=\(1-\frac{1}{4}-\frac{3}{4}\)

x^2=0

⇒x=0


Discussion

No Comment Found

Related InterviewSolutions