Question

1. The vector equations of two straight lines are r = 5i + 3j – 2k + lambda(i – 2j + 2k) and r = 2i - 11j+ak + mu(-3i – 4j + 5k). Given that the two lines intersect, find (a) the coordinates of the point of intersection, (b) the value of the constant a, (c) the acute angle between the two lines. 2. Referred to an origin O, the points A, B, C and D have coordinates (1, 1, 0), (3, 2, 5), (0, -1, -4) and (-2, -5, 0) respectively. (a) Find the vector equation of the plane passing through A, B and C. The line extit{l} passes through D and is perpendicular to the plane. (b) Find a vector equation of the line extit{l}. The line extit{l} meets the plane at the point E. (c) Find the coordinates of E.

          1. The vector equations of two straight lines are
r = 5i + 3j – 2k + lambda(i – 2j + 2k)
and
r = 2i - 11j+ak + mu(-3i – 4j + 5k).
Given that the two lines intersect, find
(a) the coordinates of the point of intersection,
(b) the value of the constant a,
(c) the acute angle between the two lines.
2. Referred to an origin O, the points A, B, C and D have coordinates (1, 1, 0), (3, 2, 5),
(0, -1, -4) and (-2, -5, 0) respectively.
(a) Find the vector equation of the plane passing through A, B and C.
The line 	extit{l} passes through D and is perpendicular to the plane.
(b) Find a vector equation of the line 	extit{l}.
The line 	extit{l} meets the plane at the point E.
(c) Find the coordinates of E.

1. The vector equations of two straight lines are
r = 5i + 3j – 2k + lambda(i – 2j + 2k)
and
r = 2i - 11j+ak + mu(-3i – 4j + 5k).
Given that the two lines intersect, find
(a) the coordinates of the point of intersection,
(b) the value of the constant a,
(c) the acute angle between the two lines.
2. Referred to an origin O, the points A, B, C and D have coordinates (1, 1, 0), (3, 2, 5),
(0, -1, -4) and (-2, -5, 0) respectively.
(a) Find the vector equation of the plane passing through A, B and C.
The line extitl passes through D and is perpendicular to the plane.
(b) Find a vector equation of the line extitl.
The line extitl meets the plane at the point E.
(c) Find the coordinates of E.

Added by Kyle M.

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