Write the distance between the parallel planes 2x − y + 3z = 4 an… - Vidyadip

Question

Write the distance between the parallel planes $2x − y + 3z = 4$ and $2x − y + 3z = 18.$

✓

Answer

The given equation are
$2x − y + 3z = 4 ....(1)$
The second equation of the plane is
$2x − y + 3z = 18 .....(2)$
We know that distance between two planes $ax + by + cz = d_1$ and $ax + by + cz = d_2$ is $\frac{|\text{d}_2-\text{d}_1|}{\sqrt{\text{a}^2+\text{b}^2+\text{c}^2}}$
So, the required distance is
$\frac{|18-4|}{\sqrt{2^2+(-1)^2+3^2}}$
$=\frac{|14|}{\sqrt{4+1+9}}$
$=\frac{14}{\sqrt{14}}$
$=\sqrt{14}\text{ units}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Solve the system of linear equation, using matrix method 2x - y = - 2; 3x + 4y = 3

Find the angle between two lines, one of which has direction ratios 2, 2, 1 while the other one is obtained by joining the points (3, 1, 4) and (7, 2, 12).

A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides down wards at the rate of 10cm/ sec, then find the rate at which the angle between the floor and ladder is decreasing when lower end of ladder is 2 metres from the wall.

Find the vector and cartesian equations of the planes:
That passes through the point (1, 0, -2) and the normal to the plane is $\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}.$

What is the value of $\cos^{-1}\Big(\cos\frac{2\pi}{3}\Big)+\sin^{-1}\Big(\sin\frac{2\pi}{3}\Big)$

Compute the magnitude of the following vectors: $\vec a = \hat i + \hat j + \hat k,\vec b = 2\hat i - 7\hat j - 3\hat k,$ $\vec c = \frac{1}{{\sqrt 3 }}\hat i + \frac{1}{{\sqrt 3 }}\hat j - \frac{1}{{\sqrt 3 }}\hat k$

If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?

Check the commutativity and associativity of the following binary operations: $ ' \ ^*\ '$ on $Q$ defined by $a ^* b = (a - b)^2$ for all $a, b \in Q.$

Write the position vector of the point which divdes the join of the points with position vectors $3\vec{\text{a}} - 2\vec{\text{b}} $ and $2\vec{\text{a}} + 3\vec{\text{b}} $ in the ratio 2 : 1.

Prove the following:
$\tan^{-1}\frac{2}{11}+\tan^{-1}\frac{7}{24}=\tan^{-1}\frac{1}{2}$