Which of the following is at a distance of sq | vedclass

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

Question

(C) The distance of a point $(x, y, z)$ from the origin $(0, 0, 0)$ is $\sqrt{x^2 + y^2 + z^2}$. For $(1, 2, 3)$,this is $\sqrt{1^2 + 2^2 + 3^2} = \sq

Vedclass · Accepted Answer

$y$-axis

Vedclass · Answer

(C) The distance of a point $(x, y, z)$ from the origin $(0, 0, 0)$ is $\sqrt{x^2 + y^2 + z^2}$. For $(1, 2, 3)$,this is $\sqrt{1^2 + 2^2 + 3^2} = \sqrt{1 + 4 + 9} = \sqrt{14}$.The distance of a point $(x, y, z)$ from the $x$-axis is $\sqrt{y^2 + z^2}$. For $(1, 2, 3)$,this is $\sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$.The distance of a point $(x, y, z)$ from the $y$-axis is $\sqrt{x^2 + z^2}$. For $(1, 2, 3)$,this is $\sqrt{1^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10}$.The distance of a point $(x, y, z)$ from the $z$-axis is $\sqrt{x^2 + y^2}$. For $(1, 2, 3)$,this is $\sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}$.Thus,the point $(1, 2, 3)$ is at a distance of $\sqrt{10}$ from the $y$-axis.

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

Similar Questions

Locate the following points in a three-dimensional Cartesian coordinate system:
$(i)$ $(1, -1, 3)$
$(ii)$ $(-1, 2, 4)$
$(iii)$ $(-2, -4, -7)$
$(iv)$ $(-4, 2, -5)$

Let $A, B, C$ be the feet of the perpendiculars from a point $P$ on the $xy, yz,$ and $zx$-planes respectively. Find the coordinates of $A, B, C$ for the following points $P$:
$(3, 4, 5), (-5, 3, 7), (4, -3, -5)$

The point $(1, -3, 4)$ lies in the octant:

The shortest distance of the point $(a, b, c)$ from the $X-$axis is:

The distance of the point $(4, 3, 5)$ from the $y$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module