4x + 8y + z – 8 = 0 and y + z – 4 = 0

NCERT Class XII Mathematics Chapter - - Solutions

Question 49 - 54: In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

Question : 54 of 78

Marks: +1, -0

Solution:

The given planes are

4x + 8y + z – 8 = 0 ...(1)

and y + z – 4 = 0...(2)

Now,

\frac{4}{0} \neq \frac{8}{1} \neq \frac{1}{1}

These planes are not parallel.

Also, (4) (0) + (8) (1) + (1) (1) ≠ 0

∴ These planes are not perpendicular.

If ‘q’ be the angle between (1) and (2), then

\cos \theta = \left| \frac{4 \times 0 + 8 \times 1 + 1 \times 1}{\sqrt{16+64+1} \sqrt{0+1+1}} \right| = \frac{1}{\sqrt{2}}

\Rightarrow \cos \theta = \frac{1}{\sqrt{2}} \Rightarrow \theta = 45^{\circ}

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