ABC is an equilateral triangle. Length of each side is a and centroid is point O . then overrightarr

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3-1.Vectors

easy

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$

$0$

$1$

$2$

$3$

Solution

$\overrightarrow{O A}, \overrightarrow{O B}$ and $\overrightarrow{O C}$ are three vectors of equal magnitude which are separated by equal angles of $120^{\circ}$. Therefore their resultant is zero.

$\overrightarrow{O A}+\overrightarrow{O A}+\overrightarrow{O C}=\overrightarrow{0}$

Standard 11

Physics

With respect to a rectangular cartesian coordinate system, three vectors are expressed as
$\vec a = 4\hat i – \hat j$, $\vec b = – 3\hat i + 2\hat j$ and $\vec c = – \hat k$
where $\hat i,\,\hat j,\,\hat k$ are unit vectors, along the $X, Y $ and $Z-$axis respectively. The unit vectors $\hat r$ along the direction of sum of these vector is

medium

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?

easy

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$ $(B)$ $\hat a + \widehat b$ $(C)$ $\hat a$ $(D)$ $\hat b$

medium

$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} – \widehat j + \widehat k$, then find their substraction by algebric method.

easy

If $\vec A$ and $\vec B$ are two non-zero vectors such that $\left| {\vec A + \vec B} \right| = \frac{{\left| {\vec A – \vec B} \right|}}{2}$ and $\left| {\vec A} \right| = 2\left| {\vec B} \right|$ then the angle between $\vec A$ and $\vec B$ is

medium

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$

Solution

Similar Questions

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following vector $(s)$ have magnitude one $(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$ $(B)$ $\hat a + \widehat b$ $(C)$ $\hat a$ $(D)$ $\hat b$

$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} – \widehat j + \widehat k$, then find their substraction by algebric method.

If $\vec A$ and $\vec B$ are two non-zero vectors such that $\left| {\vec A + \vec B} \right| = \frac{{\left| {\vec A – \vec B} \right|}}{2}$ and $\left| {\vec A} \right| = 2\left| {\vec B} \right|$ then the angle between $\vec A$ and $\vec B$ is

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If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$ $(B)$ $\hat a + \widehat b$ $(C)$ $\hat a$ $(D)$ $\hat b$