Assertion (A): No line makes angles π/6, π/4 and π/3 with the x-, y- and z-axes. Reason (R): The direction cosines l, m, n of every line satisfy l^2 + m^2 + n^2 = 1.

Question 20

MediumOriginal question

Assertion (A): No line makes angles $\frac{\pi}{6}$ , $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with the $x$ -, $y$ - and $z$ -axes.
Reason (R): The direction cosines $l, m, n$ of every line satisfy $l^{2} + m^{2} + n^{2} = 1$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\cos^{2}\frac{\pi}{6} + \cos^{2}\frac{\pi}{4} + \cos^{2}\frac{\pi}{3} = \frac{3}{4} + \frac{1}{2} + \frac{1}{4} = \frac{3}{2} \ne 1$ , so A is true.
R is true, and it is exactly the rule these angles break: R explains A.

Concept: Which triples can be direction cosines
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsDirection cosines of a line

Practise this chapter →

Ten questions from Three-Dimensional Geometry, at your own pace.

Assertion (A): No line makes angles π6\frac{\pi}{6}6π​, π4\frac{\pi}{4}4π​ and π3\frac{\pi}{3}3π​ with the xxx-, yyy- and zzz-axes.Reason (R): The direction cosines l,m,nl, m, nl,m,n of every line satisfy l2+m2+n2=1l^{2} + m^{2} + n^{2} = 1l2+m2+n2=1.

Explanation

Assertion (A): No line makes angles $\frac{\pi}{6}$ , $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with the $x$ -, $y$ - and $z$ -axes.
Reason (R): The direction cosines $l, m, n$ of every line satisfy $l^{2} + m^{2} + n^{2} = 1$ .