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NCERT Class 12- Mathematics: Chapter β 11 Three Dimensional Geometry Part 3
Question 7:
Find the coordinates of the point where the line through and crosses the plane passing through three points and
Answer:
Equation of plane through three points and is
i.e..
Equation of line through and is
Any point on line is . This point lies on plane . Therefore, , i.e.. ,
Hence the required point is .
Long Answer (L. A.)
Question 8:
Find the distance of the point from the point of intersection of the line and the plane .
Answer:
We have
Solving these two equations, we get which gives .
Therefore, the point of intersection of line and the plane is and the other given point is . Hence the distance between these two points is 13
Question 9:
A plane meets the co-ordinates axis in such that the centroid of the is the point . Show that the equation of the plane is
Answer:
Let the equation of the plane be
Then the co-ordinate of are and respectively. Centroid of the is
But co-ordinates of the centroid of the are (given) .
Therefore,
Thus, the equation of plane is
Question 10:
Find the angle between the lines whose direction cosines are given by the equations: and .
Answer:
Eliminating m from the given two equations, we get
Now if , then
and if , then .
Thus the direction ratios of two lines are proportional to and ,
i.e.. and .
So, vectors parallel to these lines are
, respectively.
If is the angle between the lines, then
Hence,