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The straight line $\frac{\mathrm{x}-3}{2}=\frac{\mathrm{y}-4}{3}=\frac{\mathrm{z}-5}{4}$ is parallel to which
one of the following ?
Options:
one of the following ?
Solution:
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Verified Answer
The correct answer is:
$4 x+4 y-5 z=0$
A plane ax $+$ by $+\mathrm{cz}=0$ is parallel to, a straight line having direction ratios $\mathrm{a}^{\prime}, \mathrm{b}^{\prime}, \mathrm{c}^{\prime}$.
If $a a^{\prime}+b b^{\prime}+c c^{\prime}=0$
In the given problem, $\mathrm{dr}_{\mathrm{s}}$ of line is $2,3,4$. We check the equations of plane in the given choices, one by one.
(a) $4 \times 2+3 \times 3+(-5) \times 4=8+9-20 \neq 0$
(b) $4 \times 2+5 \times 3+(-4) \times 4=8+15-16 \neq 0$
(c) $4 \times 2+4 \times 3+(-5) \times 4=8+12-20=0$
Further checking is not needed
If $a a^{\prime}+b b^{\prime}+c c^{\prime}=0$
In the given problem, $\mathrm{dr}_{\mathrm{s}}$ of line is $2,3,4$. We check the equations of plane in the given choices, one by one.
(a) $4 \times 2+3 \times 3+(-5) \times 4=8+9-20 \neq 0$
(b) $4 \times 2+5 \times 3+(-4) \times 4=8+15-16 \neq 0$
(c) $4 \times 2+4 \times 3+(-5) \times 4=8+12-20=0$
Further checking is not needed
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