The equation of the plane passing through the | vedclass

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

Question

(B) The equation of any plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$ is given by $A(x - 1) + B(y + 2) + C(z -

Vedclass · Accepted Answer

$4x - 8y + 7z = 41$

Vedclass · Answer

(B) The equation of any plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$ is given by $A(x - 1) + B(y + 2) + C(z - 3) = 0$,where $5A + 6B + 4C = 0$ (since the normal to the plane is perpendicular to the line direction vector $(5, 6, 4)$).Since the plane passes through the point $(4, 3, 7)$,we substitute these coordinates into the plane equation:$A(4 - 1) + B(3 + 2) + C(7 - 3) = 0$$3A + 5B + 4C = 0$.Now we have the system:$5A + 6B + 4C = 0$$3A + 5B + 4C = 0$Using cross-multiplication to solve for $A, B, C$:$\frac{A}{(6)(4) - (4)(5)} = \frac{B}{(4)(3) - (5)(4)} = \frac{C}{(5)(5) - (6)(3)}$$\frac{A}{24 - 20} = \frac{B}{12 - 20} = \frac{C}{25 - 18}$$\frac{A}{4} = \frac{B}{-8} = \frac{C}{7}$.Substituting these values into the plane equation:$4(x - 1) - 8(y + 2) + 7(z - 3) = 0$$4x - 4 - 8y - 16 + 7z - 21 = 0$$4x - 8y + 7z = 41$.

The equation of the plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$ and the point $(4, 3, 7)$ is

Similar Questions

The points $A(a, 0)$,$B(0, b)$,$C(c, 0)$,and $D(0, d)$ are such that $ac = bd$ and $a, b, c, d$ are all non-zero. Then the points:

If the best and the worst paper never appear together,then in how many ways can six examination papers be arranged?

The maximum value of $\sin (\cos (\tan x))$ is

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s) - $ velocity $(v)$ graph of this object is

$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is shown for four inductors $A, B, C$ and $D$. Which inductor has the largest value of self-inductance?

Vedclass Test Series

Exam Paper Generator

Online Exam Module