A vector $\vec{A}$ having magnitude 6 units is added to vector $\overrightarrow{\mathrm{B}}$, which is along…

A vector $\vec{A}$ having magnitude 6 units is added to vector $\overrightarrow{\mathrm{B}}$, which is along $\mathrm{x}$ -axis. The resultant of $\vec{A}$ and $\vec{B}$ is along $Y$ axis. If the magnitude of the resultant of $\vec{A}$ and $\vec{B}$ is three times that of $\vec{B}$ then magnitude of $\vec{B}$ is
  1. $\sqrt{1 \cdot 8}$
  2. $\sqrt{2 \cdot 4}$
  3. $\frac{6}{\sqrt{10}}$
  4. $\sqrt{1 \cdot 2}$

Solution

An item that has both a magnitude and a direction is called a vector. The two prime examples of vector quantities are force and velocity. Similar to how the speed of any object is related to the velocity, understanding the magnitude of the vector would show the strength of the force.
As we all know, a vector is a mathematical object that has both magnitude and direction. Now, let's say that we need to determine the length of any given vector in addition to its magnitude. The vector quantities include things like velocity, displacement, force, momentum, etc.
From the question, $A+B i=R j$ Here $R$ is the resultant vector. As given, $R=3 B$ so, $\begin{aligned} & A+B i=3 B j \\ & A=3 B j-B i \\ & A^{2}=9 B^{2}+B^{2}=10 B^{2} \\ & A=6 \\ & 36=10 B^{2} \\ & B=\sqrt{\frac{36}{10}} \\ & =\frac{6}{\sqrt{10}} \end{aligned}$

Asked in: MHT CET 2020 (20 Oct Shift 2)

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