Let the vectors overline{PQ}, overline{QR}, o | vedclass

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

Question

(C) In a regular hexagon $PQRSTU$,the sides are vectors. Let $\vec{a} = \overline{PQ}$. Then $\overline{RS}$ is parallel to $\overline{UP}$ and $\over

Vedclass · Accepted Answer

$Statement-1$ is True,$Statement-2$ is False.

Vedclass · Answer

(C) In a regular hexagon $PQRSTU$,the sides are vectors. Let $\vec{a} = \overline{PQ}$. Then $\overline{RS}$ is parallel to $\overline{UP}$ and $\overline{ST}$ is parallel to $\overline{PQ}$.Specifically,$\overline{RS} = -\overline{PQ} = -\vec{a}$ is incorrect; rather,$\overline{RS}$ is parallel to $\overline{PQ}$ but in the opposite direction,so $\overline{RS} = -\overline{PQ}$ is false. In a regular hexagon,$\overline{PQ} = \overline{UT}$ and $\overline{RS} = \overline{PQ}$ is not true. Actually,$\overline{PQ} \parallel \overline{ST}$ and $\overline{RS} \parallel \overline{UP}$.Since $\overline{PQ}$ is not parallel to $\overline{RS}$,$\overline{PQ} 	imes \overline{RS} 
eq \overrightarrow{0}$.Thus,$Statement-2$ is False because it claims $\overline{PQ} 	imes \overline{RS} = \overrightarrow{0}$.For $Statement-1$,$\overline{PQ} 	imes (\overline{RS} + \overline{ST}) = \overline{PQ} 	imes \overline{RS} + \overline{PQ} 	imes \overline{ST}$. Since $\overline{PQ}$ is not parallel to the resultant $\overline{RS} + \overline{ST}$,the cross product is non-zero. Thus,$Statement-1$ is True.

Similar Questions

The sine of the angle between the two vectors $3i + 2j - k$ and $12i + 5j - 5k$ will be

$a=3 \hat{i}+\hat{j}-\hat{k}, b=\hat{i}-4 \hat{j}+5 \hat{k}, c=4 \hat{i}+5 \hat{j}-\hat{k}$ are three vectors and a vector $r$ is perpendicular to both the vectors $b$ and $c$. If $r \cdot a=9$,then $r=$

If either $\vec{a}=\overrightarrow{0}$ or $\vec{b}=\overrightarrow{0},$ then $\vec{a} \times \vec{b}=\overrightarrow{0} .$ Is the converse true? Justify your answer with an example.

If $a = 2i + k$,$b = i + j + k$ and $c = 4i - 3j + 7k$. If $d \times b = c \times b$ and $d \cdot a = 0$,then $d$ is equal to:

Find the area of a parallelogram whose adjacent sides are given by the vectors $\vec{a} = 3\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module