Question

Find the vector equation of the plane passing through the points
i-2j +5k, -5j-k, and - 3 i + 5j.
​

Answer 1

$\textbf{Given:}$

$\textsf{Points are}$

$\mathsf{\vec{i}-2\vec{j}+5\vec{k},\;-5\vec{j}-\vec{k},\;-3\vec{i}+5\vec{j}}$

$\textbf{To find:}$

$\textsf{Vector equation of the plane passing through the points}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\boxed{\begin{minipage}{7cm} \\\textsf{Vector equation of the plane passing through}\\\\\mathsf{the\;given\;points\;\vec{a},\;\vec{b},\;\vec{c}\;is}\\\\\mathsf{\;\;\;\;\vec{r}=\vec{a}+s(\vec{b}-\vec{a})+t(\vec{c}-\vec{a})}\\ \end{minipage}}$

$\mathsf{Here,}$

$\mathsf{\vec{a}=\vec{i}-2\vec{j}+5\vec{k}}$

$\mathsf{\vec{b}=-5\vec{j}-\vec{k}}$

$\mathsf{\vec{c}=-3\vec{i}+5\vec{j}}$

$\textsf{Vector equation of the required plane is}$

$\mathsf{\vec{r}=\vec{a}+s(\vec{b}-\vec{a})+t(\vec{c}-\vec{a})}$

$\mathsf{\vec{r}=(\vec{i}-2\vec{j}+5\vec{k})+s(-5\vec{j}-\vec{k}-\vec{i}+2\vec{j}-5\vec{k})+t(-3\vec{i}+5\vec{j}-\vec{i}+2\vec{j}-5\vec{k})}$

$\implies\boxed{\mathsf{\vec{r}=(\vec{i}-2\vec{j}+5\vec{k})+s(-\vec{i}-3\vec{j}-6\vec{k})+t(-4\vec{i}+7\vec{j}-5\vec{k})}}$

$\textbf{Find more:}$

Find vector equation of plane which passes through the points (3,2,1) and (0,1,7) and is parallel to line r=2i-j+k+l(i-j-k)

https://brainly.in/question/8252354

Find the equation of the plane through (4,4,0) and perpendicular to the planes X+2y+2z=5 and 3x+3y+2z-8=0​

https://brainly.in/question/27067874