Mathematics · 2022
JEE Main · 27 July 2022, Shift 2 · Q15
If the line of intersection of the planes a x+ b y=3 and a x+ b y+ c z=0, a >0 makes an angle 30° with the plane y-z+2=0, then the direction cosines…
If the line of intersection of the planes $\displaystyle \mathrm{a} x+\mathrm{b} y=3$ and $\displaystyle \mathrm{a} x+\mathrm{b} y+\mathrm{c} z=0, \mathrm{a}>0$ makes an angle $\displaystyle 30$° with the plane $\displaystyle y-z+2=0$, then the direction cosines of the line are :
Official answer
(1)
$\displaystyle \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$
(2)
$\displaystyle \frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}, 0$
NTA’s answer key accepts either.
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.