Exam Style C4 Vectors Questions - Solutions · Exam Style C4 Vectors Questions - Solutions 1) a) We use the equation (As ) (Simplifying the direction vector) or written as b) To find
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3) a) At point B the vector equations for the lines are equal. Thus:
(This leads us to the equations)
[1]
[2] [3]
Generally, one solves equations [1] & [2] simultaneously and substitute into equation [3] to find the values of λ and µ. Fortunately, this question has an easy route. Taking equation [3]:
Substituting this into the line equation for l1.
b) To find the angle, we use the equation:
It is important to note that the vectors that are dotted together must be the direction components of the lines only.
d) It is often best to draw a diagram to visualise how best to answer this question.
There are many ways in which one can answer this question, but the best way to answer this question is to use trigonometry. Since the shortest line linking point C to the line l1 will meet the line l1 at a right angle, we have a right angle triangle. Thus: Distance = (Thus determining )