If the vectors represented by the sides AB an | vedclass

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

Question

(A) In a regular hexagon $ABCDEF$,let the center be $O$. Given $\overrightarrow{AB} = a$ and $\overrightarrow{BC} = b$. In $	riangle ABC$,by triangle

Vedclass · Accepted Answer

$2\,b - a$

Vedclass · Answer

(A) In a regular hexagon $ABCDEF$,let the center be $O$. Given $\overrightarrow{AB} = a$ and $\overrightarrow{BC} = b$. In $	riangle ABC$,by triangle law of vector addition,$\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC} = a + b$. Since $O$ is the center,$\overrightarrow{AO} = \overrightarrow{OC} = \frac{1}{2}\overrightarrow{AC} = \frac{1}{2}(a + b)$. Also,$\overrightarrow{AF} = \overrightarrow{OC} = \frac{1}{2}(a + b)$ and $\overrightarrow{FE} = \overrightarrow{AB} = a$. Now,in $	riangle AFE$,by triangle law of vector addition,$\overrightarrow{AE} = \overrightarrow{AF} + \overrightarrow{FE}$. Substituting the values,$\overrightarrow{AE} = \frac{1}{2}(a + b) + a = \frac{1}{2}a + \frac{1}{2}b + a = \frac{3}{2}a + \frac{1}{2}b$. Wait,let us re-evaluate using the property of the hexagon: $\overrightarrow{AE} = \overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} + \overrightarrow{DE}$. Alternatively,$\overrightarrow{AE} = \overrightarrow{AD} + \overrightarrow{DE}$. Since $\overrightarrow{AD} = 2\overrightarrow{BC} = 2b$ and $\overrightarrow{DE} = -\overrightarrow{AB} = -a$,Therefore,$\overrightarrow{AE} = 2b - a$.

If the vectors represented by the sides $AB$ and $BC$ of the regular hexagon $ABCDEF$ are $a$ and $b$ respectively,then the vector represented by $\overrightarrow{AE}$ will be

Similar Questions

If $D, E, F$ are the midpoints of the sides $BC, CA$ and $AB$ of the triangle $ABC$,then $\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF}$ is:

Three non-zero non-collinear vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$, and $3\vec{b}+2\vec{c}$ is collinear with $\vec{a}$. Then $\vec{a}+3\vec{b}+2\vec{c}$ equals to

$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

Classify the following measure as a scalar or a vector:
$20 \text{ m/s}$ towards north

In the given figure (a square),identify the following vectors:
Equal vectors.

Vedclass Test Series

Exam Paper Generator

Online Exam Module