Equation of a Plane : Point Normal Form

Q.

Draw the graph of the following linear equations in two variables: $2x+y=3$

Q.

The coordinate of the point of intersection of the line $\frac{[x-1]}{1}=\frac{[y+2]}{3}=\frac{[z-2]}{-2}$ with the plane $3x+4y+5z-25=0$ is

1. $(5,10,6)$

2. $(10,5,6)$

3. $(5,5,-6)$

4. $(5,10,-6)$

Q.

Equation of the plane passing through the intersection of the planes $x+y+z=6$, $2x+3y+4z+5=0$ and the point $(1,1,1)$ is

1. $20x+23y+26z–69=0$

2. $31x+45y+49z+52=0$

3. $8x+5y+2z–69=0$

4. $4x+5y+6z–7=0$

Q.

Find the equation of line in vector and in cartesian form that passes through the point with position vector $2\hat{i}-\hat{j}+4\hat{k}$ and is in the direction $\hat{i}+2\hat{j}-\hat{k}$

Q.

Use the graph to write a linear function that relates $\mathrm{y}$ to $\mathrm{x}$.

Q. Let $P$ be the plane containing the line $L_1:y+z=2,$ $x=0$ and is parallel to the line $L_2:x-z=2,y=0.$ If the distance of the plane $P$ from the origin is $d$ units, then the value of $3d^2$ is

Q. P is a fixed point (a, a, a) on a line through the origin equally inclined to the axes, then any plane through P perpendicular to OP, makes intercepts on the axes, the sum of whose reciprocals is equal to

1. a
2. $\frac{3}{2a}$
3. $\frac{3a}{2}$
4. $\frac{1}{a}$

Q.

Match the two columns:

Column I	COLUMN II
(A) $4x+3y=12$ cuts $x$ and $y$ axes	(p) $4x-3y=7$
(B) $4-3x=0$ can be written as	(q) at $\left(3,0\right)$ and $\left(0,4\right)$
(C) $\left(3,4\right)$ lies on $3y=ax+7$, then $a$ =	(r) $-3x+0y+4=0$
(D) $\left(1,-1\right)$ is a solution of the equation	(s) $\frac{5}{3}$

Choose the correct option

1. $\left(A\right)\to q;\left(B\right)\to r;\left(C\right)\to s;\left(D\right)\to p$

2. $\left(A\right)\to p;\left(B\right)\to r;\left(C\right)\to s;\left(D\right)\to q$

3. $\left(A\right)\to q;\left(B\right)\to r;\left(C\right)\to p;\left(D\right)\to s$

4. $\left(A\right)\to r;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to s$

Q.

Find the equation of a line with $x$-intercept = $5$ and passing through the point $(4,-7)$

Q.

The distance of the point (1, 3, -7) from the plane passing through the point (1, -1, -1) having normal perpendicular to both the lines
$\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$, is

1. $\frac{20}{\sqrt{74}}$ units

2. $\frac{10}{\sqrt{83}}$ units

3. $\frac{5}{\sqrt{83}}$ units

4. $\frac{10}{\sqrt{74}}$ units