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Vector Equation for Straight Line

Which of the ...

Question

$Which of the following is the vector equation of a line which passes through point P (2, - 1, 4) and having the direction along the vector ˆ i + 3 ˆ j - 2 ˆ k .$

(2 + λ) ˆ i + (- 1 + 3 λ) ˆ j + (4 - 2 λ) ˆ k

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(2 - λ) ˆ i + (- 1 - 3 λ) ˆ j + (4 + 2 λ) ˆ k

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(1 + 2 λ) ˆ i + (3 - λ) ˆ j + (- 2 + 4 λ) ˆ k

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λ ˆ i + 3 λ ˆ j - 2 λ ˆ k

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Solution

The correct option is A
$(2 + λ) ˆ i + (- 1 + 3 λ) ˆ j + (4 - 2 λ) ˆ k$
The vector equation of a line passing through a point 'a' and in the direction of vector 'b' is given by
$\to V = \to a + λ \to b$ Here,
$\to a = 2 ˆ i - ˆ j + 4 ˆ k$
and $\to b = ˆ i + 3 ˆ j - 2 ˆ k$
$\to V = 2 ˆ i - ˆ j + 4 ˆ k + λ (ˆ i + 3 ˆ j - 2 ˆ k) = (2 + λ) ˆ i + (- 1 + 3 λ) ˆ j + (4 - 2 λ) ˆ k$

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Similar questions

Which of the following is the vector equation of a line which passes through point P (2, - 1, 4) and having the direction along the vector ˆ i + 3 ˆ j - 2 ˆ k .

\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{c} = λ \hat{i} - \hat{j} + λ \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{c} = λ \hat{i} + λ \hat{j} + 5 \hat{k}

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = 3 \hat{i} + λ \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} + 2 \hat{k}

\vec{a} = \hat{i} + 3 \hat{j}, \vec{b} = 5 \hat{k}, \vec{c} = λ \hat{i} - \hat{j}

\vec{a} and \vec{b}

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 4 \hat{i} - 9 \hat{j} + 2 \hat{k}

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 5 \hat{i} - 9 \hat{j} + 2 \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} and \vec{b} = 3 \hat{i} + 2 \hat{j} - λ \hat{k}

\vec{a} = λ \hat{i} + 3 \hat{j} + 2 \hat{k} and \vec{b} = \hat{i} - \hat{j} + 3 \hat{k}

λ \hat{i} + \hat{j} + 2 \hat{k}, \hat{i} + λ \hat{j} - \hat{k} and 2 \hat{i} - \hat{j} + λ \hat{k}

r = i - j + 2 k + λ (i - 2 j + 3 k)

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