Write the ratio in which the plane 4x + 5y − 3z = 8 divides the l… - Vidyadip

Question

Write the ratio in which the plane 4x + 5y − 3z = 8 divides the line segment joining the points (−2, 1, 5) and (3, 3, 2).

✓

Answer

We know that the ratio in which the plane ax + by + cz + d = 0 divides the line sebment joining
(x₁, y₁, z₁) and (x₂, y₂, z₂) is $\frac{-(\text{ax}_1+\text{by}_1+\text{cz}_1+\text{d})}{\text{ax}_2+\text{by}_2+\text{cz}_2+\text{d}}$
Here, a = 4,b = 5,c = -3,d = -8,x₁ = -2,y₁ = 1,z₁ = 5,x₂ = 3,y₂ = 3,z₂ = 2
So, the required ratio
$=\frac{-(4(-2)+5(1)-3(5)-8)}{4(3)+5(3)-3(2)-8}$
$=\frac{-(-8+5-15-8)}{12+15-6-8}$
$=\frac{26}{13}$
$=\frac{2}{1}$ or $2 :1.$

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" from The plane→The plane — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate:
$\cos\Big(\tan^{-1}\frac{3}{4}\Big)$

Find the principal values of each of the following:
$\text{cosec}^{-1}\big(-\sqrt2\big)$

Differentiate the function $\frac{\cos ^{-1} \frac{x}{2}}{\sqrt{2 x+7}},-2<x<2$ w.r.t to x.

Solve the following equation for x:
$3\sin^{-1}\frac{2\text{x}}{1+\text{x}^2}-4\cos^{-1}\frac{1-\text{x}^2}{1+\text{x}^2}+2\tan^{-1}\frac{2\text{x}}{1-\text{x}^2}=\frac{\pi}{3}$

Write the following in the simplest form:
$\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}+1}{\text{x}}\Big\},\text{x}\neq0$

Find the area of the parallelogram determinrd by the vectors:
$2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}}$ and $\hat{\text{i}}-\hat{\text{j}}$

Let A = {-1, 0, 1, 2}, B = {-4, -2, 0, 2} and f, g : A $\rightarrow$ B be the functions defined by f(x) = x² - x, x $\in$ A and $g(x) = 2\left| {x - \frac{1}{2}} \right| - 1,x \in A$. Are f and g equal? Justify your answer.
(Hint: One may note that two functions f : A $\rightarrow$ B and g : A $\rightarrow$ B such that f(a) = g(a) $\forall$ a $\in$ A, are called equal functions).

Find the solution of the differential equation $\text{x}\sqrt{1+\text{y}^{2}}\text{dx}+\text{y}\sqrt{1+\text{x}^{2}}\text{dy}=0.$

If $A = \begin{bmatrix} 2 & -3 & \\ 3 & 4 & \\ \end{bmatrix} $ show that $\text{A^{2} - 6 A + 17 I = 0.}$ Hense find $A^{-1}.$

Prove the following Exercise:
$\int^{\frac{\pi}{2}}_{0}2\tan^{3}\text{x dx}=1-\log2$