For a parallelogram ABCD,if L and M are mid-p | vedclass

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

Question

(B) Let the position vectors of vertices $A, B, C, D$ be $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ respectively.Since $ABCD$ is a parallelogram,$\vec{d} =

Vedclass · Accepted Answer

$\frac{3}{2} AC$

Vedclass · Answer

(B) Let the position vectors of vertices $A, B, C, D$ be $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ respectively.Since $ABCD$ is a parallelogram,$\vec{d} = \vec{a} + \vec{c} - \vec{b}$.$L$ is the mid-point of $BC$,so $\vec{l} = \frac{\vec{b} + \vec{c}}{2}$.$M$ is the mid-point of $CD$,so $\vec{m} = \frac{\vec{c} + \vec{d}}{2} = \frac{\vec{c} + (\vec{a} + \vec{c} - \vec{b})}{2} = \frac{\vec{a} + 2\vec{c} - \vec{b}}{2}$.Now,$\vec{AL} = \vec{l} - \vec{a} = \frac{\vec{b} + \vec{c}}{2} - \vec{a} = \frac{\vec{b} + \vec{c} - 2\vec{a}}{2}$.And $\vec{AM} = \vec{m} - \vec{a} = \frac{\vec{a} + 2\vec{c} - \vec{b}}{2} - \vec{a} = \frac{2\vec{c} - \vec{b} - \vec{a}}{2}$.Adding these,$\vec{AL} + \vec{AM} = \frac{\vec{b} + \vec{c} - 2\vec{a} + 2\vec{c} - \vec{b} - \vec{a}}{2} = \frac{3\vec{c} - 3\vec{a}}{2} = \frac{3}{2}(\vec{c} - \vec{a}) = \frac{3}{2} \vec{AC}$.Thus,$AL + AM = \frac{3}{2} AC$.

For a parallelogram $ABCD$,if $L$ and $M$ are mid-points of $BC$ and $CD$ respectively,then $AL + AM =$

Similar Questions

Let $ABC$ be a triangle. Let $u = \vec{AB}$ and $v = \vec{AC}$. If $D$ is the midpoint of $BC$,then $\vec{AD} =$

If $C$ is the mid-point of line segment $AB$ and $P$ is any point not on the line $AB$,then

If $\vec{a} = 4\hat{i} + 3\hat{j}$ and $\vec{b} = 2\hat{i} + \lambda\hat{j}$ are parallel vectors,then the value of $\lambda$ is:

Find a vector of magnitude $11$ in the direction opposite to that of $\overrightarrow{PQ}$,where $P$ and $Q$ are the points $(1,3,2)$ and $(-1,0,8)$ respectively.

If $a$ is collinear with $b = 3 \hat{i} + 6 \hat{j} + 6 \hat{k}$ and $a \cdot b = 27$,then $|a| =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module