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  • ind the vector and cartesian equations of the line which is perpendicular to the lines with equations <img alt="\frac{x + 2}{1} =\frac{ y - 3}{2} = \frac{z + 1}{4}" src="https://learn.caree

ind the vector and cartesian equations of the line which is perpendicular to the lines with equations

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

and passes through the point (1, 1, 1). Also find the angle between the given lines.

 

 

Answers (1)

best_answer

\vec{n}=\vec{d}_1 \times \vec{d}_2=\langle-4,4,-1\rangle

\begin{aligned} &\vec{r}=\langle 1,1,1\rangle+\lambda\langle-4,4,-1\rangle\\ &\frac{x-1}{-4}=\frac{y-1}{4}=\frac{z-1}{-1} \end{aligned}

\cos \theta=\frac{\vec{d}_1 \cdot \vec{d}_2}{\left|\vec{d}_1\right|\left|\vec{d}_2\right|}=\frac{24}{\sqrt{21 \times 29}} \Rightarrow \theta \approx 13.46^{\square}

Posted by

Divya Sharma

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