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GUJCET 2025 Math Paper

Question : 2 of 40

Marks: +1, -0

(5, -2, 4)

3\hat{i}-2\hat{j}+8\hat{k}

is . . . . . . .

Solution:

Concept:

The Cartesian equation of a line is formed using a point on the line and its direction ratios.

Explanation:

For a line through

(x_1,y_1,z_1)

and parallel to

a\hat{i}+b\hat{j}+c\hat{k}

, the equation is

\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}

Here, the point is

(x_1,y_1,z_1)=(5,-2,4)

The direction ratios are

a=3

b=-2

c=8

Substitute these values into the formula.

This gives

\frac{x-5}{3}=\frac{y-(-2)}{-2}=\frac{z-4}{8}

Simplify

y-(-2)

y+2

So the required equation is

\frac{x-5}{3}=\frac{y+2}{-2}=\frac{z-4}{8}

Answer:

\frac{x-5}{3}=\frac{y+2}{-2}=\frac{z-4}{8}

, which matches option A.

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