KC Sinha Solution Class 12 Chapter 30 3D Geometry : Plane (त्रिविमीय ज्यामिति : समतल ) Exercise 30.1 (Q51-Q58)

 Exercise 30.1


Question 51

Find the distance of a point (2,5,-3) from the plane $\vec{r} \cdot(6 \hat{i}-3 \hat{j}+2 \hat{k})=4$

Sol :



Question 52

If a plane has intercepts a, b, c on axes and is at a distance of p units from the origin, then prove that

$\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{p^{2}}$

Sol :


Question 53

Find the distance between the point P(6,5,9) and the plane determined by the points A(3,-1,2), B(5,2,4) and C(-1,-1,6)

Sol :




Question 54

Find the distance between the planes 2x+3y+4z=4 and 4x+6y+8z=12.

Sol :



Question 55

Find the equation of the line of intersection of the planes x-2y+z=1 and x+2y-2z=5 in symmetric form.

Sol :



TYPE-X

Question 56

Find the equation of the line through point (1,2,3) and parallel to line x-y+2z=5, 3x+y+z=6

Sol :


Question 57

Prove that the lines x=ay+b, z=cy+d and $x=a^{\prime} y+b, z=c^{\prime} y+d^{\prime}$ are mutually perpendicular if $a a^{\prime}+c c^{\prime}=-1$

Sol :


Question 58

Find the vector equation of the line passing through (1,2,3) and parallel to the planes $\vec{r} \cdot(\hat{i}-\hat{j}+2 \hat{k})=5$ and $\vec{r} \cdot(3 \hat{i}+\hat{j}+\hat{k})=6$.

Sol :







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