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Answer the following.
There are two solar panels, A and B placed parallel to each other on the terrace of a building. The…
There are two solar panels, A and B placed parallel to each other on the terrace of a building. The equation of the surface of the panel A is $2x + 2y - z + 9 = 0$.
The direction cosines of the plane are:
- (1)$\left(\dfrac{-2}{3}, \dfrac{-2}{3}, \dfrac{1}{3}\right)$
- (2)$\left(\dfrac{2}{3}, \dfrac{-2}{3}, \dfrac{-1}{3}\right)$
- (3)$\left(\dfrac{2}{3}, \dfrac{2}{3}, \dfrac{1}{3}\right)$
- (4)$\left(\dfrac{-2}{3}, \dfrac{-2}{3}, \dfrac{-1}{3}\right)$
Answer
Answer
AICorrect option: (1)
Answer: (1) $\left(\dfrac{-2}{3}, \dfrac{-2}{3}, \dfrac{1}{3}\right)$
Write the plane as $-2x - 2y + z = 9$ (constant on the right-hand side positive). The normal $(-2, -2, 1)$ has length $\sqrt{4 + 4 + 1} = 3$, so the direction cosines are $\left(\dfrac{-2}{3}, \dfrac{-2}{3}, \dfrac{1}{3}\right)$.
From ISC 2025 Improvement Mathematics Paper 1, question 15(ii)(a).
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