Find the coordinates of the point where the line through (5,1,6) and (3,4,1) crosses the ZX-plane.
Find the coordinates of the point where the line through (5,1,6)and (3,4,1) crosses the YZ plane.
Find the shortest distance between lines \(\overrightarrow{r}\)=\(6\hat i+2\hat j+2\hat k\)+λ(\(\hat i+2\hat j+2\hat k\))and\(\overrightarrow{r}\)=-\(-4\hat i-\hat k\)+μ(\(3\hat i+2\hat j+2\hat k\)).
Find the equation of the plane passing through (a,b,c)and parallel to the plane \(\overrightarrow{r}\).(\(\hat i+\hat j+\hat k\))=2.
Find the vector equation of the plane passing through (1,2,3)and perpendicular to the plane r→.(i^+2j^-5k^)+9=0.