The angle between the planes 2x-y+z=6\: and\: x+y +2z=7 \: is

  • Option 1)

    30^{\circ}

  • Option 2)

    45^{\circ}

  • Option 3)

    0^{\circ}

  • Option 4)

    60^{\circ}

 

Answers (1)

As we learnt in

Angle between two planes (Cartesian form) -

Let the two planes be

ax+by+cz+d=0\: and \: a_{1}x+b_{1}y+c_{1}z+d_{1}=0

then the angle between them is defined as the angle between their normals

\cos \Theta = \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}

-

 

 \cos \Theta = \frac{2\times 1+ (-1)X1+1\times2}{\sqrt{4+1+1 \ }\sqrt{1+1+4}}

\frac{3}{6}=\frac{1}{2}

\Theta = 60^{\circ} 

 


Option 1)

30^{\circ}

Incorrect

Option 2)

45^{\circ}

Incorrect

Option 3)

0^{\circ}

Incorrect

Option 4)

60^{\circ}

correct

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