If the foot of the perpendicular from (0,0,0) | vedclass

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

Question

(A) The normal vector $\vec{n}$ to the plane is the vector joining the origin $(0,0,0)$ to the foot of the perpendicular $(1,2,3)$.$\vec{n} = (1-0)\ha

Vedclass · Accepted Answer

$x+2y+3z=14$

Vedclass · Answer

(A) The normal vector $\vec{n}$ to the plane is the vector joining the origin $(0,0,0)$ to the foot of the perpendicular $(1,2,3)$.$\vec{n} = (1-0)\hat{i} + (2-0)\hat{j} + (3-0)\hat{k} = \hat{i} + 2\hat{j} + 3\hat{k}$.The equation of a plane passing through a point $(x_0, y_0, z_0)$ with normal vector $\vec{n} = a\hat{i} + b\hat{j} + c\hat{k}$ is given by $a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$.Substituting the point $(1,2,3)$ and the normal vector $(1,2,3)$,we get:$1(x-1) + 2(y-2) + 3(z-3) = 0$$x - 1 + 2y - 4 + 3z - 9 = 0$$x + 2y + 3z - 14 = 0$$x + 2y + 3z = 14$.

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$,then the equation of the plane is

Similar Questions

The total number of valence electrons in $4.2 \, g$ of $N_3^-$ ion is ......... $N_A$. ($N_A$ = Avogadro number)

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

The reaction sequence given below is carried out with $16$ moles of $X$. The yield of the major product in each step is given below the product in parentheses. The amount $($in grams$)$ of $S$ produced is $.....$
image
Use: Atomic mass $($in amu$): H =1, C =12, O =16, Br =80$

The common bottle cork is a product of .......... .

What is the biological concentration of $DDT$ in the body fat of Indian people?

Vedclass Test Series

Exam Paper Generator

Online Exam Module