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

The value of $k$ for which the planes $3x - 6y - 2z = 7$ and $2x + y - kz = 5$ are perpendicular to each other,is

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of $\triangle ABC$ is at the point $(1, 2, 3)$,then the equation of the plane is

The vector equation of the plane containing the point $(1, -1, 2)$ and perpendicular to the planes $2x + 3y - 2z = 5$ and $x + 2y - 3z = 8$ is:

Consider the three planes $P_{1}: 3x + 15y + 21z = 9$; $P_{2}: x - 3y - z = 5$; and $P_{3}: 2x + 10y + 14z = 5$. Then,which one of the following is true?

In $3$-dimensional space,the equation $x^2-8x+12=0$ represents ....

Vedclass Test Series

Exam Paper Generator

Online Exam Module