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
$(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ 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 $, a = 4,b = 5,c = -3,d = -8,x_1 = -2,y_1 = 1,z_1 = 5,x_2 = 3,y_2 = 3,z_2 = 2$
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 Question" from The plane→The plane — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Differentiate the following functions with respect to x:
$\tan^{-1}(\text{e}^{\text{x}})$

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

If f(x) = |x|, prove that fof = f.

Differentiate the following w.r.t. x:
$\tan^{-1}\Big(\frac{3\text{a}^2\text{x}-\text{x}^3}{\text{a}^3-3\text{ax}^2}\Big),\frac{-1}{\sqrt{3}}<\frac{\text{x}}{\text{a}}<\frac{1}{\sqrt{3}}$

Show that the lines $\frac{\text{x}-5}{7}=\frac{\text{y}+2}{-5}=\frac{\text{z}}{1}$ and $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$ are perpendicular to each other.

Write the value of $\cos^2\Big(\frac{1}{2}\cos^{-1}\frac{3}{5}\Big).$

Find the area of a triangle having the points A(1, 1, 1), B(1, 2, 3) and C(2, 3, 1) as its vertices.

Evaluate the following integrals:
$\int\frac{\sin2\text{x}}{(\text{a}+\text{b}\cos2\text{x})^2}\text{dx}$

Let X represents the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are possible values of X?

Find the area of the parallelogram determinrd by the vectors:
$3\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ and $\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$