BPSC 47th Exam Prelims 2005 Solved Paper

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Question : 129 of 150

Marks: +1, -0

The acute angle between the normals to the planes

2x – y + 2 = 6

and

x + y + 2z = 7

is –

$x /2$
$x/ 4$
$x/ 3$
$x /6$

Solution:

2 x-y+z=6

x+y+2 z=7

∵ \cos θ=\;{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}/{√{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} √{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}

=\;{2(1)+(-1)(1)+1(2)}/{√{4+1+1} √{4+1+1}}

=\;{2-1+2}/{6}=\;{3}/{6}=\;{1}/{2}

=\cos \;{π}/{3}

⇒ θ=\;{π}/{3}

∴

Acute angle

=\;{π}/{3}

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