The equation of a line passing through the points 3i + 4j and i + 2j can be given by $\to r = (1 + 2 λ) i + (2 + 2 λ) j . H e r e λ ϵ I R$

True

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False

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Solution

The correct option is A
True

We already know the equation of a line passing through the points $\to a a n d \to b$ and is parallel to $\to a - \to b$ and can be given by $\to r = \to a + λ (\to a - \to b)$ . Here the points are 3i + 4j and i +2j. Therefore equation of line will be, $\to r = i + 2 j + λ ((3 i + 4 j) - (i + 2 j)) \to r = i + 2 j + λ (2 i + 2 j) \to r = (1 + 2 λ) i + (2 + 2 λ) j$ .

The given statement is true.

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The equation of a line passing through the points 3i + 4j and i + 2j can be given by $\to r = (1 + 2 λ) i + (2 + 2 λ) j . H e r e λ ϵ I R$

Vector equation of a straight line passing through a point given by position vector $¯ a$ parallel to $¯ b$ be is given by $¯ r = ¯ a - λ ¯ b, w h e r e ¯ r$ , where $¯ r$ is r position vector of a general point on the line and $λ ϵ I R$

Q. Find equation of a line passing through the point

(3, 1, 2)

and perpendicular to the lines

¯ ¯ ¯ r = (1 + λ) ¯ i + (2 + 2 λ) ¯ j + (3 + 3 λ) ¯ ¯ ¯ k

and

¯ ¯ ¯ r = (- 3 λ) ¯ i + (2 λ) ¯ j + (5 λ) ¯ ¯ ¯ k

Q. Determine the equation of plane through the point

a = (i + 2 j - k)

and prependicular to the line of intersection of planes

r . (3 i - j + k) = 1

and

r . (i + 4 j - 2 k) = 2.

Q. Find the vector equation of the plane passing through the points

3 \hat{i} + 4 \hat{j} + 2 \hat{k}, 2 \hat{i} - 2 \hat{j} - \hat{k} and 7 \hat{i} + 6 \hat{k} .

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The equation of a line passing through the points 3i + 4j and i + 2j can be given by →r=(1+2λ)i+(2+2λ)j.Here λϵIR

The equation of a line passing through the points 3i + 4j and i + 2j can be given by $\to r = (1 + 2 λ) i + (2 + 2 λ) j . H e r e λ ϵ I R$