Exercise 30.1
Question 21
Find the equation of the plane through (3,4,-1) which is parallel to the plane $\vec{r} \cdot(2 \hat{i}-3 \hat{j}+5 \hat{k})+7=0$
Sol :
Question 22
Find the equation of the plane passing through (a, b, c) and parallel to the plane $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2$.
Sol :
Question 23
(i) Find the equation of the plane passing through the point (3,-3,1) and perpendicular to the line joining (3,4,-1) and (2,-1,5).
(ii) Find the equation of the plane passing through the points (3,4,1) and (0,1,0) and parallel to the line $\frac{x+3}{2}=\frac{y-3}{7}=\frac{z-2}{5}$
Sol :
Question 24
Find the vector and cartesian equation of the plane which passes through the point (5,2,-4) and perpendicular to the line with direction ratios (2,3,-1).
Sol :
Question 25
Find the equation of the plane through the point (1,4,-2) and parallel to the plane -2x+y-3z=7
Sol :
Question 26
Find the equation of the plane through the points (2,-3,1) and (5,2,-1) and perpendicular to the plane x-4y+5z+2=0.
Sol :
Question 27
Find the equation of the plane through the points (-1,1,1) and (1,-1,1) and perpendicular to the plane x+2y+2z=5.
Sol :
Question 28
Find the equation of the plane passing through the point (1,1,-1) and perpendicular to the planes x+2y+3z-7=0 and 2x-3y+4z=0.
Sol :
TYPE-V
Question 29
Find the equation of a plane through the points (2,1,0), (3,-2,-2) and (3,1,7).
Sol :
Question 30
Find the equation of the plane that passes through three points (1,1,0) , (1,2,1), (-2,2,-1).
Sol :
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