Question

The angle between the planes 2x – y + z = 6 and

x + y + 2z = 7 is

• A. p
• B. $\frac{2\pi}{3}$
• C. $\frac{\pi}{2}$
• D. $\frac{\pi}{3}$

Answer 1

Answer: (D)

$\frac{\pi}{3}$

Answer 2

Apply cos q =$\frac{a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}}\sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$

Here a₁, b₁, c₁

Ž 2, –1, 1

a₂ , b₂, c₂ Ž 1, 1, 2

\ cos q = $\frac{2(1) + 1( - 1) + 1(2)}{\sqrt{6}\sqrt{6}} = \frac{3}{6}$

cos q = $\frac{1}{2} = \theta = \frac{\pi}{3}$