2007 H2 Mathematics

Paper 1 Question 8

The line $l$ passes through the points $A$ and $B$ with coordinates $(1, 2, 4)$ and $(- 2, 3, 1)$ respectively.

The plane $p$ has equation $3 x - y + 2 z = 17 .$ Find

(a)

the coordinates of the point of intersection of $l$ and $p,$

[5]

(b)

The acute angle between $l$ and $p,$

[3]

(c)

The perpendicular distance from $A$ to $p .$

[3]