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 $\to r = (1 + 2 λ) i + (2 + 2 λ) j . H e r e λ ϵ I R$

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

3 ¯ i + 4 ¯ j - 7 ¯ ¯ ¯ k, ¯ i - ¯ j + 6 ¯ ¯ ¯ k

a = (i + 2 j - k)

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

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

3 \to i + 4 \to j + 2 \to k, 2 \to i - 2 \to j - \to k

7 \to i + \to k

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