The position vectors of two points P and Q ar | vedclass

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

Question

(C) Given position vectors of points $P$ and $Q$ are $\vec{p} = 3i + j + 2k$ and $\vec{q} = i - 2j - 4k$. The vector $\overrightarrow{PQ} = \vec{q} -

Vedclass · Accepted Answer

$r \cdot (2i + 3j + 6k) = -28$

Vedclass · Answer

(C) Given position vectors of points $P$ and $Q$ are $\vec{p} = 3i + j + 2k$ and $\vec{q} = i - 2j - 4k$. The vector $\overrightarrow{PQ} = \vec{q} - \vec{p} = (i - 2j - 4k) - (3i + j + 2k) = -2i - 3j - 6k$. The plane passes through $Q$ and is perpendicular to $\overrightarrow{PQ}$. The normal vector to the plane is $\vec{n} = \overrightarrow{PQ} = -2i - 3j - 6k$. The equation of the plane is given by $(r - \vec{q}) \cdot \vec{n} = 0$,which is $r \cdot \vec{n} = \vec{q} \cdot \vec{n}$. $\vec{q} \cdot \vec{n} = (i - 2j - 4k) \cdot (-2i - 3j - 6k) = (1)(-2) + (-2)(-3) + (-4)(-6) = -2 + 6 + 24 = 28$. Thus,$r \cdot (-2i - 3j - 6k) = 28$,which can be written as $r \cdot (2i + 3j + 6k) = -28$.

The position vectors of two points $P$ and $Q$ are $3i + j + 2k$ and $i - 2j - 4k$ respectively. The equation of the plane passing through $Q$ and perpendicular to $PQ$ is:

Similar Questions

The equations of planes parallel to the plane $x+2y+2z+8=0$,which are at a distance of $2$ units from the point $(1,1,2)$ are

The equation of the plane passing through $(1, -1, 2)$ and perpendicular to the planes $x + 2y - 2z = 4$ and $3x + 2y + z = 6$ is:

Let the foot of the perpendicular drawn from the point $(1, 2, 3)$ to a plane be $(-1, 3, -2)$. Then the perpendicular distance from the origin to the plane is

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2x-y-2z=5$ and $3x-6y+2z=7$ is

If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module