Let alpha, beta, gamma be distinct real numbe | vedclass

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

Question

(B) Let the points be $P$,$Q$,and $R$ with position vectors $\vec{p} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k}$,$\vec{q} = \beta \hat{i} + \ga

Vedclass · Accepted Answer

an equilateral triangle

Vedclass · Answer

(B) Let the points be $P$,$Q$,and $R$ with position vectors $\vec{p} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k}$,$\vec{q} = \beta \hat{i} + \gamma \hat{j} + \alpha \hat{k}$,and $\vec{r} = \gamma \hat{i} + \alpha \hat{j} + \beta \hat{k}$.The distance $PQ = |\vec{q} - \vec{p}| = \sqrt{(\beta - \alpha)^2 + (\gamma - \beta)^2 + (\alpha - \gamma)^2}$.The distance $QR = |\vec{r} - \vec{q}| = \sqrt{(\gamma - \beta)^2 + (\alpha - \gamma)^2 + (\beta - \alpha)^2}$.The distance $RP = |\vec{p} - \vec{r}| = \sqrt{(\alpha - \gamma)^2 + (\beta - \alpha)^2 + (\gamma - \beta)^2}$.Since $PQ = QR = RP$,the points form an equilateral triangle.

Let $\alpha, \beta, \gamma$ be distinct real numbers. The points with position vectors $\alpha \hat{i} + \beta \hat{j} + \gamma \hat{k}$,$\beta \hat{i} + \gamma \hat{j} + \alpha \hat{k}$,and $\gamma \hat{i} + \alpha \hat{j} + \beta \hat{k}$ form:

Similar Questions

In a quadrilateral $ABCD$,$M$ and $N$ are the mid-points of the sides $AB$ and $CD$ respectively. If $\vec{AD} + \vec{BC} = t \vec{MN}$,then $t =$

If $\bar{a}, \bar{b}, \bar{c}$ are the position vectors of the points $A(1,3,0), B(2,5,0), C(4,2,0)$ respectively and $\bar{c}=t_{1} \bar{a}+t_{2} \bar{b}$,then the value of $t_{1} t_{2}$ is:

$a, b, c$ are non-coplanar vectors. If $a+3 b+4 c=x(a-2 b+3 c)+y(a+5 b-2 c)+z(6 a+14 b+4 c)$,then $x+y+z=$

If the position vectors of the points $A$ and $B$ are $2 \hat{i}+3 \hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+2 \hat{k}$ respectively,then the unit vector along $\overrightarrow{BA}$ and in the direction of $\overrightarrow{AB}$ is

If $ABCDEF$ is a regular hexagon,where two adjacent sides $\vec{AB}$ and $\vec{BC}$ are $\vec{a}$ and $\vec{b}$ respectively. Then $\vec{CD}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module