Find the distance between the following pairs | vedclass

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

Question

(A) The distance between points $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ is given by the formula:$PQ = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The distance between points $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ is given by the formula:$PQ = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} + (z_{2}-z_{1})^{2}}$Given points are $(2, 3, 5)$ and $(4, 3, 1)$.Substituting the values into the formula:$PQ = \sqrt{(4-2)^{2} + (3-3)^{2} + (1-5)^{2}}$$PQ = \sqrt{(2)^{2} + (0)^{2} + (-4)^{2}}$$PQ = \sqrt{4 + 0 + 16}$$PQ = \sqrt{20}$$PQ = 2 \sqrt{5}$

Find the distance between the following pairs of points: $(2, 3, 5)$ and $(4, 3, 1)$. (in $\sqrt{5}$)

Similar Questions

Find the coordinates of a point on the $y$-axis which is at a distance of $5\sqrt{2}$ from the point $P(3, -2, 5)$.

$A$ point is on the $x$-axis. What are its $y$-coordinate and $z$-coordinate?

Which of the following is at a distance of $\sqrt{10}$ from the point $(1, 2, 3)$?

$A$ point $(x, y, z)$ moves parallel to the $x$-axis. Which of the three variables $x, y, z$ remain fixed?

Let $A, B, C$ be the feet of perpendiculars from a point $P$ on the $x, y, z$-axes respectively. Find the coordinates of $A, B$ and $C$ for the following points $P$:
$(i)$ $(3, 4, 2)$
$(ii)$ $(-5, 3, 7)$
$(iii)$ $(4, -3, -5)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module