Given that overrightarrow A + overrightarrow B + overrightarrow C= 0 out of three vectors two are eq

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3-1.Vectors

hard

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C= 0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt 2 $ times that of either of the two having equal magnitude. Then the angles between vectors are given by

$30°, 60°, 90°$

$45°, 45°, 90°$

$45°, 60°, 90°$

$90°, 135°, 135°$

Solution

(d) From polygon law, three vectors having summation zero should form a closed polygon. (Triangle) since the two vectors are having same magnitude and the third vector is $\sqrt 2 $ times that of either of two having equal magnitude. i.e. the triangle should be right angled triangle

Angle between $A$ and $B$, $\alpha$ $= 90°$

Angle between $B$ and $C$, $\beta$ $= 135°$

Angle between $A$ and $C$, $\gamma$ $= 135°$

Standard 11

Physics

Given that $P + Q + R =0$. Which of the following statement is true?

medium

Given that; $A = B = C$. If $\vec A + \vec B = \vec C,$ then the angle between $\vec A$ and $\vec C$ is $\theta _1$. If $\vec A + \vec B+ \vec C = 0,$ then the angle between $\vec A$ and $\vec C$ is $\theta _2$. What is the relation between $\theta _1$ and $\theta _2$ ?

medium

What is the angle between $\overrightarrow P $ and the resultant of $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P – \overrightarrow Q )$

easy

A body is moving under the action of two forces ${\vec F_1} = 2\hat i – 5\hat j\,;\,{\vec F_2} = 3\hat i – 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by

medium

The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to

medium

(KVPY-2009)

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C= 0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt 2 $ times that of either of the two having equal magnitude. Then the angles between vectors are given by

Solution

Similar Questions

Given that $P + Q + R =0$. Which of the following statement is true?

Given that; $A = B = C$. If $\vec A + \vec B = \vec C,$ then the angle between $\vec A$ and $\vec C$ is $\theta _1$. If $\vec A + \vec B+ \vec C = 0,$ then the angle between $\vec A$ and $\vec C$ is $\theta _2$. What is the relation between $\theta _1$ and $\theta _2$ ?

What is the angle between $\overrightarrow P $ and the resultant of $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P – \overrightarrow Q )$

A body is moving under the action of two forces ${\vec F_1} = 2\hat i – 5\hat j\,;\,{\vec F_2} = 3\hat i – 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by

The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to

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