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  • State True and False for the given statement: The equation of a line, which is parallel to vec{r}=( 5 hat{i}-4hat{j}+6hat{k} )+lambda( 3hat{i}+7hat{j}+2hat{k} )and which passes through (5, -2, 4) is frac{x-5}{2}=frac{y+2}{-1}=frac{z-4}{3}

State True and False for the given statement:

The equation of a line, which is parallel to 2 \hat{i}+\hat{j}+3\hat{k} and which passes through (5, -2, 4) is \frac{x-5}{2}=\frac{y+2}{-1}=\frac{z-4}{3}

Answers (1)

We know, the equation of a line in Cartesian form is

\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}

, where a, b and c are the direction ratios and (x1, y1, z1) is a     particular point on the line.

The given line is parallel to therefore it has 2, 1, 3 as direction ratios.

(a = 2, b = 1, c = 3)

The line passes through (5, -2, 4)

Substituting these values, we get the equation of line:

\frac{x-5}{2}=\frac{y+2}{1}=\frac{z-4}{3}

Thus, the given statement is False.

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infoexpert24

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