Write the equations for the x and y-axes.

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:

We are required to write the equations of the coordinate axes.

Equation of the x-axis

Every point on the x-axis has y-coordinate equal to 0.

∴ Equation of the x-axis is:

y = 0

Equation of the y-axis

Every point on the y-axis has x-coordinate equal to 0.

∴ Equation of the y-axis is:

x = 0

Final Answer:

Equation of x-axis: y = 0
Equation of y-axis: x = 0

Write the equations for the x and y-axes.

Solution and Explanation

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