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Chapter 16: Problem 1489
If vector \(\underline{r}\) forms an angle \(\alpha, \beta, \gamma\) with \(\mathrm{x}, \mathrm{y}, \mathrm{z}\) -axis then \(\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=\) (A) 1 (B) 2 (C) \(-1\) (D) \(-2\)
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The Equation of line passing through \((1,2,1)\) and \([(2 \mathrm{x}-1) / 3]=[(1-\mathrm{y}) / 3]=[(3 \mathrm{z}-2) / 5] \mathrm{is}\) (A) \([(2 \mathrm{x}-2) / 3]=[(2-\mathrm{y}) / 3]=[(3 \mathrm{z}-3) / 5]\) (B) \([(2 x+2) / 3]=[(2+y) / 3]=[(3 z+3) / 5]\) (C) \([(2 x-1) /(-3)]=[(1-y) /(-3)]=[(3 z-2) /(-1)]\) (D) None of these
Line \([\\{\sqrt{(2) x-3 \sqrt{2}\\} / 1]}=[\\{2 \sqrt{2}-\sqrt{(2) \mathrm{y}\\} / 2], \mathrm{z}+1}=0\) direction cosine (A) \((1 / \sqrt{5}),-(2 \overline{/ \sqrt{5}}), 0\) (B) \(-(1 / \sqrt{5}),(1 / \sqrt{5}), 0\) (C) \((1 / \sqrt{5}), 0,(1 / \sqrt{5})\) (D) \((1 / \sqrt{5}),-(1 / \sqrt{5}), 0\)
\(\mathrm{P}(1,6,3)\) to \((\mathrm{x} / 1)=[(\mathrm{y}-1) / 2]=[(\mathrm{z}-2) / 3]\) on then image of \(\mathrm{P}\) is (A) \(\overline{(-1,0,-7)}\) (B) \((-1,0,7)\) (C) \((1,0,7)\) (D) \((1,0,-7)\)
If any vector forms angles \((\pi / 4),(\pi / 3)\) and \((\pi / 6)\) with axis, then such vector with measure 4 unit is (A) \((2,2 \sqrt{3}, 2 \sqrt{2})\) (B) \(\overline{(-2},-2 \sqrt{3}, 2 \sqrt{2})\) (C) \((2,2 \sqrt{3},-2 \sqrt{2})\) (D) \((-2,-2 \sqrt{3},-2 \sqrt{2})\)
Angle between two diagonal of the cube is (A) \(\cos ^{-1}(1 / \sqrt{3})\) (B) \(\cos ^{-1}(1 / 3)\) (C) \(\cos ^{-1}(1 / 9)\) (D) \(\cos ^{-1}(\sqrt{3} / 2)\)
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