Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#6
Relative to an origin , the position vectors of points and are given by
i. Find the value of and hence state whether angle AOB is acute, obtuse or a right angle.
ii. The point is such that . Find the unit vector in the direction of OX.
We recognize that is angle between and .
Hence we use scalar/dot product of and . We have both and .
The scalar or dot product of two vectors and in component form is given as;
For the given case;
If and & , then and are perpendicular.
If , then angle between and is acute.
If , then angle between and is obtuse.
Therefore angle AOB is obtuse.
From the given condition;
We need to substitute in above equation to find .
A vector in the direction of is;
Therefore, for the given case;
Hence, we can write;
A unit vector in the direction of is;
Now, unit vector in the direction of can be found as follows.
Hence, we need . This can be found from as follows.
We can find as follows;