Specialist2025 Exam 2 Section A · Q15CAS active1 mark

Angle between two planes

Consider the two planes described by the equations $2x + 2y + z = 2$ and $ax + 4z = 1$ , where $a$ is a positive constant.

The angle between the two planes is $\cos^{-1}\left(\frac{2}{3}\right)$ .

The value of $a$ satisfies the equation

1 mark

a+2=\sqrt{a^2+16}

\frac{2a+4}{3\sqrt{a^2+16}}=\frac{3}{2}

2a+4=3\sqrt{a^2+16}

\frac{2a+4}{\sqrt{a^2+16}}=\frac{2}{3}

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