If overrightarrow{a}, overrightarrow{b}, over | vedclass

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

Question

(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.We can rewrite this as $\ov

Vedclass · Accepted Answer

plane

Vedclass · Answer

(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.We can rewrite this as $\overrightarrow{r} = \overrightarrow{a} - p\overrightarrow{a} - q\overrightarrow{a} + p\overrightarrow{b} + q\overrightarrow{c}$.Rearranging the terms, we get $\overrightarrow{r} - \overrightarrow{a} = p(\overrightarrow{b} - \overrightarrow{a}) + q(\overrightarrow{c} - \overrightarrow{a})$.This is the parametric form of the equation of a plane passing through the point with position vector $\overrightarrow{a}$ and parallel to the vectors $(\overrightarrow{b} - \overrightarrow{a})$ and $(\overrightarrow{c} - \overrightarrow{a})$.Since $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are non-coplanar, the vectors $(\overrightarrow{b} - \overrightarrow{a})$ and $(\overrightarrow{c} - \overrightarrow{a})$ are linearly independent, thus defining a unique plane.

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three non-coplanar vectors, then the vector equation $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$ represents a :

Similar Questions

$A$ plane meets the coordinate axes at $A, B, C$ and $(\alpha, \beta, \gamma)$ is the centroid of the triangle $ABC$. Then the equation of the plane is

Find the equation of the plane passing through the intersection of the planes $3x - y + 2z - 4 = 0$ and $x + y + z - 2 = 0$ and the point $(2, 2, 1)$.

$A$ plane $\pi$ passes through the points $(5,1,2)$, $(3,-4,6)$, and $(7,0,-1)$. If $p$ is the perpendicular distance from the origin to the plane $\pi$ and $l, m, n$ are the direction cosines of a normal to the plane $\pi$, then $|3l+2m+5n|=$

The equation of the plane which is parallel to the $y$-axis and cuts off intercepts of length $2$ and $3$ from the $x$-axis and $z$-axis respectively is:

Find the equation of the plane passing through $(a, b, c)$ and parallel to the plane $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module