KC Sinha Solution Class 12 Chapter 30 3D Geometry : Plane (त्रिविमीय ज्यामिति : समतल ) Exercise 30.1 (Q1-Q10)

 Exercise 30.1

Question 1

Find the cartesian equations of the following planes whose vector equations are

(i) $\vec{r} \cdot(3 \hat{i}+3 \hat{j}-4 \hat{k})=0$

(ii) $\vec{r} \cdot(2 \hat{i}-7 \hat{j}+4 \hat{k})+1=0$

(iii) $\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=2$

(iv) $\vec{r} \cdot[(s-2 t) \hat{i}+(3-t) \hat{j}+(2 s+t) \hat{k}]=15$

Sol :

Question 2

Find the vector equation of the following planes whose cartesian equations are

(i) $2x+3 y-z-1=0$

(ii) $x+2 y+3 z+5=0$

(iii) $x-3 y+6 z=0$

Sol :

Question 3

Find the equation of the plane with intercepts 2 , 3 and 4 on the x, y and z-axes respectively.

Sol :

Question 4

Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.

Sol :

Question 5

Find the equation of the plane which cuts intercepts 2, 3 -4  on the axes.

Sol :

Question 6

Find the intercepts of the plane 3x+4y-7z=84 on the axes. Also find the length of perpendicular from origin to this line and direction cosines of this normal.

Sol :

Question 7

Find the intercepts cut off on the axes by the plane 2x+y-z=5.

Sol :

Question 8

Find the equation of the plane which meets the axes in A, B, C given that the centroid of ΔABC is the point (α ,β ,ɣ).

Sol :

Question 9

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector $3 \hat{i}+5 \hat{j}-6 \hat{k}$.

Sol :

Question 10

Find the vector equation of the plane which is at a distance of $\frac{6}{\sqrt{29}}$ from the origin is $2 \hat{i}-3 \hat{j}+4 \hat{k}$. Also find its cartesian equation.

Sol :