The plane frac{x}{a} + frac{y}{b} + frac{z}{c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The equation of the plane is $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 3$.To find the intersection with the $x$-axis,set $y=0$ and $z=0$: $\frac{

Vedclass · Accepted Answer

$(a, b, c)$

Vedclass · Answer

(D) The equation of the plane is $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 3$.To find the intersection with the $x$-axis,set $y=0$ and $z=0$: $\frac{x}{a} = 3 \implies x = 3a$. So,$A = (3a, 0, 0)$.To find the intersection with the $y$-axis,set $x=0$ and $z=0$: $\frac{y}{b} = 3 \implies y = 3b$. So,$B = (0, 3b, 0)$.To find the intersection with the $z$-axis,set $x=0$ and $y=0$: $\frac{z}{c} = 3 \implies z = 3c$. So,$C = (0, 0, 3c)$.The centroid of a triangle with vertices $(x_1, y_1, z_1), (x_2, y_2, z_2),$ and $(x_3, y_3, z_3)$ is given by $\left( \frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3} \right)$.Substituting the coordinates of $A, B,$ and $C$:Centroid $= \left( \frac{3a+0+0}{3}, \frac{0+3b+0}{3}, \frac{0+0+3c}{3} \right) = (a, b, c)$.

The plane $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 3$ meets the coordinate axes at points $A, B,$ and $C$. The centroid of the triangle $ABC$ is:

Similar Questions

The equation of the plane passing through the points $(2,3,1)$ and $(4,-5,3)$ and parallel to the $y$-axis is:

The equation of the plane passing through $(-1, 1, 2)$ whose normal makes equal acute angles with the coordinate axes is:

Let the plane passing through the point $(-1, 0, -2)$ and perpendicular to each of the planes $2x + y - z = 2$ and $x - y - z = 3$ be $ax + by + cz + 8 = 0$. Then the value of $a + b + c$ is equal to:

What is the equation of the plane passing through the point $(1, 1, 0)$ and perpendicular to the line $\vec{r} = (2, 3, 4) + k(3, 4, 5)$,where $k \in R$?

Let $(\alpha, \beta, \gamma)$ be the image of the point $P (2, 3, 5)$ in the plane $2x + y - 3z = 6$. Then $\alpha + \beta + \gamma$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module