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Consider the following statements:
1 . Equations ax $+b y+c z+d=0, a^{\prime} x+b^{\prime} y+c^{\prime} z+d^{\prime}=0$
represent a straight line.
2 . Equation of the form
$\frac{\mathrm{x}-\alpha}{\ell}=\frac{\mathrm{y}-\beta}{\mathrm{m}}=\frac{\mathrm{z}-\gamma}{\mathrm{n}}$
represent a straight line passing through the point $(\alpha, \beta, \gamma)$ and having direction ratio proportional to $l, \mathrm{~m}, \mathrm{n}$. Which of the statements given above is/are correct?
Options:
1 . Equations ax $+b y+c z+d=0, a^{\prime} x+b^{\prime} y+c^{\prime} z+d^{\prime}=0$
represent a straight line.
2 . Equation of the form
$\frac{\mathrm{x}-\alpha}{\ell}=\frac{\mathrm{y}-\beta}{\mathrm{m}}=\frac{\mathrm{z}-\gamma}{\mathrm{n}}$
represent a straight line passing through the point $(\alpha, \beta, \gamma)$ and having direction ratio proportional to $l, \mathrm{~m}, \mathrm{n}$. Which of the statements given above is/are correct?
Solution:
1573 Upvotes
Verified Answer
The correct answer is:
Both 1 and 2
Equations $a x+b y+c z+d=0, a^{\prime} x+b^{\prime} y+c^{\prime} z+d^{\prime}=0$
represent a straight line and equation of the form $\frac{x-\alpha}{\ell}=\frac{y-\beta}{m}=\frac{z-y}{n}$
represent a straight line passing through the point $(\alpha, \beta, \gamma)$ and having direction ratios proportional to $l, \mathrm{~m}$
n. Thus, both statements are correct.
represent a straight line and equation of the form $\frac{x-\alpha}{\ell}=\frac{y-\beta}{m}=\frac{z-y}{n}$
represent a straight line passing through the point $(\alpha, \beta, \gamma)$ and having direction ratios proportional to $l, \mathrm{~m}$
n. Thus, both statements are correct.
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