Browse Questions

# True or False: The equation of aline,which is parallel to $2\hat i\;-\hat j\;+\hat 3k$ and which passes through the point (5,-2,4) is $\Large \frac{x-5}{2}\;=\frac{y-2}{-1}\;=\frac{z-4}{3}.$

$\begin{array}{1 1}True \\ False \end{array}$

Toolbox:
• Cartesian equation of a line passing through a point and parallel to a given vector is $\large\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$
Let the vector which is parallel to the given line be $\overrightarrow b=2 \hat i+\hat j+ 3\hat k$
Let the position vector $\overrightarrow a=5 \hat i-2\hat j+ 4\hat k$
Hence Cartesian equation of a line passing through a point and parallel to a given vector is
$\large\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$
Hence $(x_1,y_1,z_1)$ are $(5,-2,4)$ and $(l,m,n)$ are $(2,+1,3)$
Therefore The equation of the line is
$\large\frac{x-5}{2}=\frac{y+2}{-1}=\frac{z-4}{3}$
Hence it is a $False$ statement