Vector Problems involving Points & Lines
Exercises for students:
Solve the following problems and check your working using the above applet:
The point A has coordinates (3, -1, 2) and the line L has equation r = 2i - k + t (i + j + 2k).
Find the coordinates of the point B on L such that AB is perpendicular to L.
The line L passes through the point P with position vector 2i - k and is parallel to i + j + 2k.
Find the length of the projection of OP onto L.
The line L has cartesian equation x - 2 = (y - 4) / 2 = (z - 1) / 2. The point A has position vector i + 2j + 3k.
Find the exact value of the length of the perpendicular from A to L.
L1 denotes the line with cartesian equation (x - 3) / 2 = (y - 1) / 3 = (z - 2) / 3.
L2 denotes the line which passes through the point (1, 2, 1) and is parallel to the vector 2i - j + k.
Prove that L1 and L2 intersect, and find the coordinates of the point of intersection.
Calculate the acute angle between L1 and L2, giving your answer correct to the nearest 0.1°.
Right-click here to download a Summary of Vectors.
Right-click here to download a Summary of Vectors with Examples.
Right-click here to download this page and the Java Class File.
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