NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 2
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11.2 Solved Examples
Short Answer (S.A)
Question 1: If the direction ratios of a line are , find the direction cosines of the line.
Answer:
The direction cosines are given by
Here are respectively.
Therefore,
are D.C’s of the line.
Question 2:
Find the direction cosines of the line passing through the points and .
Answer:
The direction cosines of a line passing through the points and are
Here
Hence D.C.’s are
Question 3: If a line makes an angle of with the positive direction of , respectively, then find its direction cosines.
Answer:
The direction cosines of a line which makes an angle of with the , are
Therefore, D.C.’s of the line are i.e.,
Question 4:
The coordinate of a point on the line joining the points and is . Find its coordinate.
Answer:
Let the point P divide in the ratio , then the co-ordinate of are
But coordinate of P is . Therefore,
Hence, the coordinate of is
Question 5: Find the distance of the point whose position vector is from the plane
Answer:
Here
So, the required distance is
Question 6:
Find the distance of the point from the line

Find the Distance of the Point
Answer:
Here is the given point.
Any point on the line is given by ,
.
Since , we have
Thus
Hence .