(A) The vector $\vec{AB}$ is given by $(3-2, 5-3, -3-(-1)) = (1, 2, -2)$.The vector $\vec{CD}$ is given by $(3-1, 5-2, 7-3) = (2, 3, 4)$.The projectio

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(A) The vector $\vec{AB}$ is given by $(3-2, 5-3, -3-(-1)) = (1, 2, -2)$.The vector $\vec{CD}$ is given by $(3-1, 5-2, 7-3) = (2, 3, 4)$.The projection of vector $\vec{AB}$ on vector $\vec{CD}$ is given by the formula $\frac{\vec{AB} \cdot \vec{CD}}{|\vec{CD}|}$.First,calculate the dot product $\vec{AB} \cdot \vec{CD} = (1)(2) + (2)(3) + (-2)(4) = 2 + 6 - 8 = 0$.Since the dot product is $0$,the projection of $AB$ on $CD$ is $0$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

Easy

If the coordinates of the points $A, B, C, D$ are $(2, 3, -1), (3, 5, -3), (1, 2, 3)$ and $(3, 5, 7)$ respectively,then the projection of $AB$ on $CD$ is

A
$0$
B
$1$
C
$2$
D
$\sqrt{3}$

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THREE DIMENSIONAL GEOMETRY

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System of co-ordinates, Direction cosines and direction ratios, Projection

The angle between the lines,whose direction cosines $l, m, n$ satisfy the equations $l+m+n=0$ and $2l^2+2m^2-n^2=0$,is (in $^{\circ}$)

MediumMHT CET 2023

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Find the angle between two lines whose direction cosines are given by the relations $l + m + n = 0$ and $l^2 + m^2 - n^2 = 0$.

Difficult

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Which of the following can not be the direction cosines of a line?

EasyMHT CET 2019

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If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is

MediumMHT CET 2017

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The number of straight lines that are equally inclined to the three-dimensional coordinate axes is

Easy

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If the coordinates of the points $A, B, C, D$ are $(2, 3, -1), (3, 5, -3), (1, 2, 3)$ and $(3, 5, 7)$ respectively,then the projection of $AB$ on $CD$ is

Similar Questions

The angle between the lines,whose direction cosines $l, m, n$ satisfy the equations $l+m+n=0$ and $2l^2+2m^2-n^2=0$,is (in $^{\circ}$)

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