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 :
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