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Question: What is the symmetric form of the line passing through the point (1, -2,3) and having the direction ...

What is the symmetric form of the line passing through the point (1, -2,3) and having the direction ratios 2, -3, 4?

A

x+12=y−2−3=z+34\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z+3}{4}

B

x−1−2=y+23=z−3−4\frac{x-1}{-2}=\frac{y+2}{3}=\frac{z-3}{-4}

C

x+1−2=y−23=z+3−4\frac{x+1}{-2}=\frac{y-2}{3}=\frac{z+3}{-4}

D

x−12=y+2−3=z−34\frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-3}{4}

Answer

x−12=y+2−3=z−34\frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-3}{4}

Explanation

Solution

The symmetric form of the equation of a line passing through a point (x1,y1,z1)(x_1, y_1, z_1) and having direction ratios (a,b,c)(a, b, c) is given by:

x−x1a=y−y1b=z−z1c\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}

Given the point (x1,y1,z1)=(1,−2,3)(x_1, y_1, z_1) = (1, -2, 3) and direction ratios (a,b,c)=(2,−3,4)(a, b, c) = (2, -3, 4), substitute these values into the formula:

x−12=y−(−2)−3=z−34\frac{x - 1}{2} = \frac{y - (-2)}{-3} = \frac{z - 3}{4}

x−12=y+2−3=z−34\frac{x - 1}{2} = \frac{y + 2}{-3} = \frac{z - 3}{4}