Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

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:

A line cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Step 1: Write the intercept form of a line

The intercept form of a line is:

x/a + y/b = 1

Since the intercepts are equal,

a = b

So the equation becomes:

x/a + y/a = 1

or

x + y = a

Step 2: Use the given point (2, 3)

Substitute x = 2 and y = 3:

2 + 3 = a

a = 5

Final Answer:

The equation of the required line is:
x + y = 5

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Solution and Explanation

Top Questions on Various Forms of the Equation of a Line