Find the equation of the line which passes though (0, 0) with slope m.

Question

If the components of \( \vec{a} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k} \) along and perpendicular to \( \vec{b} = 3\hat{i} + \hat{j} - \hat{k} \) respectively are \( \frac{16}{11} (3\hat{i} + \hat{j} - \hat{k}) \) and \( \frac{1}{11} (-4\hat{i} - 5\hat{j} - 17\hat{k}) \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is equal to:

Answer 1

Given:

The line passes through the point (0, 0)
Slope of the line = m

Step 1: Use point–slope form of a line

Equation of a line:

y − y₁ = m(x − x₁)

Here,

(x₁, y₁) = (0, 0)

y − 0 = m(x − 0)

Step 2: Simplify

y = mx

Final Answer:

The equation of the required line is:
y = mx

Find the equation of the line which passes though (0, 0) with slope m.

Solution and Explanation

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