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 :
No comments:
Post a Comment