Three Dimensional Geometr Y
Find the angle between the lines whose direction ratios are a, b, c and b - c, c - a, a - b.
Find the equation of a line parallel to x-axis and passing through the origin.
If the lines 1 2 3 1 1 6 and3 2 2 3 1 5
| x | y | z | x | y | z |
|---|
k k / − − − − − −= = = =− − are perpendicular, find the value of k.
Find the shortest distance between lines ˆ ˆˆ ˆ ˆ ˆ6 2 2 ( 2 2 )= + + + λ − +/arrowrightnospr i j k i j k and ˆ ˆˆ ˆ ˆ4 (3 2 2 )= − − + µ − −/arrowrightnospr i k i j k .
Find the vector equation of the line passing through the point (1, 2, - 4) and perpendicular to the two lines: 7/10 16/19 8 −=− +=− z y x and 15 x − = 29 5 8 5 y z− − = − .