Line L_1 passes through the point (1,2,3) and is parallel to z-axis.

Question

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to $z$-axis. Line $L_2$ passes through the point $(\lambda, 5,6)$ and is parallel to $y$

Accepted Answer

$$\begin{aligned}
& 3=\frac{|[(\lambda-1) \hat{i}+3 \hat{j}+3 \hat{k}] .(\hat{k} \times \hat{j})|}{|\hat{k} \times \hat{j}|}=|\lambda-1|=3 \
& \Rightarrow \lambda=4 \text { or }-2, \lambda_2<\lambda_1 \Rightarrow \lambda_2=-2 \
& \lambda_1=4
\end{aligned}$$

$$\begin{aligned}
& (3,-4,4-k) \perp \hat{k} \
& 4-k=0 \Rightarrow k=4 \
& \Rightarrow \text { Distance between }(4,-2,7) &(1,2,7) \
& \Rightarrow \sqrt{3^2+4^2}=5
\end{aligned}$$

Solutions · 1