Let \(\bar{a}\) = 3i – 4j – 5k, b = 2i – 3j + k
(i) Vector Equation is \(\bar{r}\) = \(\bar{a}\)+ λ(\(\bar{b}\) –\(\bar{a}\) )\(\bar r\)
= 3i – 4j – 5k + λ( – i + j + 6k)
Cartesian Equation is
= \(\frac{x-3}{-1}=\frac{y+4}{1}=\frac{z+5}{6 }\)
(ii) Let the point be (x, y, 0)
\(\frac{x-3}{-1}=\frac{y+4}{1}=\frac{z+5}{6 }\)
= \(x= \frac{13}{6},y = \frac{-19}{6 }\)
Then the point on the XY Plane is
\(\frac{13}{6},\frac{-19}{6}\),0