A variable point on a line has the coordinates r-1-r-3-r-2-4 where -r- is any real number- Then the d-r-s of the line are-

Let P=(r+1,r 3,r√(2)+4) Let A,B are points on the line when r=0,r=1 respectively nbsp;∴ r=0 ⇒ nbsp; A(1, 3,4) and r=1⇒ B(2, 2,√(2)+4) ∴ d.r's of AB is (1,1 ...

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Standard XII

Mathematics

Condition for Concurrency of Three Lines

A variable po...

Question

A variable point on a line has the coordinates $(r + 1, r - 3, r \sqrt{2} + 4)$ where ' $r$ ' is any real number. Then the d.r's of the line are:

\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}

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(1, - 3, \sqrt{2})

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(1, - 3, 4)

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(1, 1, \sqrt{2})

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Solution

The correct option is D $(1, 1, \sqrt{2})$
Let $P = (r + 1, r - 3, r \sqrt{2} + 4)$
Let $A, B$ are points on the line when $r = 0, r = 1$ respectively
$∴ r = 0$ $\Rightarrow A (1, - 3, 4)$ and
$r = 1 \Rightarrow B (2, - 2, \sqrt{2} + 4)$
$∴$ d.r's of $A B$ is $(1, 1, \sqrt{2})$

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A variable point on a line has the coordinates (r+1,r−3,r√2+4) where 'r' is any real number. Then the d.r's of the line are:

The correct option is D (1,1,√2)Let P=(r+1,r−3,r√2+4) Let A,B are points on the line when r=0,r=1 respectively ∴r=0 ⇒A(1,−3,4) and r=1⇒B(2,−2,√2+4) ∴ d.r's of AB is (1,1,√2)

A variable point on a line has the coordinates $(r + 1, r - 3, r \sqrt{2} + 4)$ where ' $r$ ' is any real number. Then the d.r's of the line are:

The correct option is D $(1, 1, \sqrt{2})$
Let $P = (r + 1, r - 3, r \sqrt{2} + 4)$
Let $A, B$ are points on the line when $r = 0, r = 1$ respectively
$∴ r = 0$ $\Rightarrow A (1, - 3, 4)$ and
$r = 1 \Rightarrow B (2, - 2, \sqrt{2} + 4)$
$∴$ d.r's of $A B$ is $(1, 1, \sqrt{2})$