If the x-coordinate of a point P on the line | vedclass

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

Question

(B) Let the point $P$ divide the line segment $QR$ in the ratio $\lambda : 1$.The coordinates of $P$ are given by the section formula as $\left( \frac

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(B) Let the point $P$ divide the line segment $QR$ in the ratio $\lambda : 1$.The coordinates of $P$ are given by the section formula as $\left( \frac{5\lambda + 2}{\lambda + 1}, \frac{2\lambda + 2}{\lambda + 1}, \frac{-2\lambda + 1}{\lambda + 1} \right)$.Given that the $x$-coordinate of $P$ is $4$,we have:$\frac{5\lambda + 2}{\lambda + 1} = 4$Solving for $\lambda$:$5\lambda + 2 = 4(\lambda + 1)$$5\lambda + 2 = 4\lambda + 4$$\lambda = 2$Now,substitute $\lambda = 2$ into the expression for the $z$-coordinate of $P$:$z = \frac{-2\lambda + 1}{\lambda + 1} = \frac{-2(2) + 1}{2 + 1} = \frac{-4 + 1}{3} = \frac{-3}{3} = -1$.Thus,the $z$-coordinate of $P$ is $-1$.

If the $x$-coordinate of a point $P$ on the line joining the points $Q(2, 2, 1)$ and $R(5, 2, -2)$ is $4$,then the $z$-coordinate of $P$ is:

Similar Questions

The resultant gate and its Boolean expression in the given circuit is

If $\vec{a}, \vec{b}$ and $\vec{c}$ are vectors with magnitudes $2, 3$ and $4$ respectively,then the best upper bound of $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ among the given values is

Electrons from excited chlorophyll molecule of photosystem $II$ are accepted first by

Mass $M$ is divided into two parts $xM$ and $(1-x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

Vedclass Test Series

Exam Paper Generator

Online Exam Module