On which of the following lines does the poin | vedclass

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

Question

(C) Let the general point on the line $\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1} = \lambda$ be $(2\lambda + 4, 2\lambda + 5, \lambda + 3)$.S

Vedclass · Accepted Answer

$\frac{x - 1}{1} = \frac{y - 3}{2} = \frac{z + 4}{-5}$

Vedclass · Answer

(C) Let the general point on the line $\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1} = \lambda$ be $(2\lambda + 4, 2\lambda + 5, \lambda + 3)$.Since this point lies on the plane $x + y + z = 2$,we substitute the coordinates into the plane equation:$(2\lambda + 4) + (2\lambda + 5) + (\lambda + 3) = 2$$5\lambda + 12 = 2$$5\lambda = -10 \implies \lambda = -2$.Substituting $\lambda = -2$ back into the coordinates,we get the point of intersection $P = (2(-2) + 4, 2(-2) + 5, -2 + 3) = (0, 1, 1)$.Now,we check which line passes through the point $(0, 1, 1)$ by substituting $x=0, y=1, z=1$ into the given options.For option $C$: $\frac{0 - 1}{1} = -1$,$\frac{1 - 3}{2} = -1$,$\frac{1 + 4}{-5} = -1$.Since all ratios are equal to $-1$,the point $(0, 1, 1)$ lies on the line given in option $C$.

On which of the following lines does the point of intersection of the line $\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1}$ and the plane $x + y + z = 2$ lie?

Similar Questions

Solid $NaCl$ is a bad conductor of electricity since

$\int_0^{\pi / 2} \frac{200 \sin x+100 \cos x}{\sin x+\cos x} d x$ is equal to (in $\pi$)

For better survival of the human population,which of the following steps is most important?

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12})(1+x^{24})$ is

$A$ big water drop is formed by the combination of $n$ small water drops of equal radii. The ratio of the surface energy of $n$ drops to the surface energy of the big drop is

Vedclass Test Series

Exam Paper Generator

Online Exam Module