A, B, C, D, E are five coplanar points,then o | vedclass

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

Question

(B) Given that $A, B, C, D, E$ are five coplanar points.We need to evaluate the sum: $\overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC}

Vedclass · Accepted Answer

$3\,\overrightarrow{DE}$

Vedclass · Answer

(B) Given that $A, B, C, D, E$ are five coplanar points.We need to evaluate the sum: $\overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} + \overrightarrow{AE} + \overrightarrow{BE} + \overrightarrow{CE}$.By using the triangle law of vector addition,we know that $\overrightarrow{PQ} + \overrightarrow{QR} = \overrightarrow{PR}$.Rearranging the terms in the given expression:$= (\overrightarrow{DA} + \overrightarrow{AE}) + (\overrightarrow{DB} + \overrightarrow{BE}) + (\overrightarrow{DC} + \overrightarrow{CE})$Applying the triangle law to each group:$= \overrightarrow{DE} + \overrightarrow{DE} + \overrightarrow{DE}$$= 3\,\overrightarrow{DE}$.

$A, B, C, D, E$ are five coplanar points,then $\overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} + \overrightarrow{AE} + \overrightarrow{BE} + \overrightarrow{CE}$ is equal to

Similar Questions

If the points with position vectors $(\alpha \hat{i}+10 \hat{j}+13 \hat{k})$,$(6 \hat{i}+11 \hat{j}+11 \hat{k})$,and $(\frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k})$ are collinear,then $(19 \alpha-6 \beta)^2=$

$PQRS$ is a quadrilateral and $PQ=a, QR=b, SP=a-b$. $M$ is the mid-point of $QR$ and $X$ is a point on $SM$ such that $SX=\frac{4}{5}SM$. If $SM=m(4a-b)$ and $SX=n(4a-b)$,then $m+n=$

If the vectors $\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$ and $\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$ are collinear,then the values of $p$ and $q$ are:

If the coordinates of points $A, B, C,$ and $D$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6),$ and $(2, 9, 2)$ respectively,then the angle between $AB$ and $CD$ is:

If $2 \hat{i}+\hat{j}-\hat{k}$,$\hat{i}-3 \hat{j}+5 \hat{k}$ and $-3 \hat{i}+4 \hat{j}+4 \hat{k}$ are the position vectors of three points $A$,$B$ and $C$ respectively,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module