Three vectors and each of magnitude are acting as shown in figure. The resultant of the three vectors is , The value of is

Question

Three vectors $\vec{O P}, \vec{O Q}$ and $\vec{O R}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$ , The value of $x$ is ______ . [2024]

Smart Achievers · Accepted Answer

(3)

$\vec{R} = (A + \frac{A}{\sqrt{2}}) \hat{i} + (A - \frac{A}{\sqrt{2}}) \hat{j}$

$| \vec{R} |$ $= \sqrt{{(A + \frac{A}{\sqrt{2}})}^{2} + {(A - \frac{A}{\sqrt{2}})}^{2}} = \sqrt{3} A$

Solution

Q.
Three vectors $\vec{O P}, \vec{O Q}$ and $\vec{O R}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$ , The value of $x$ is ______ . [2024]

Ans.
(3)

$\vec{R} = (A + \frac{A}{\sqrt{2}}) \hat{i} + (A - \frac{A}{\sqrt{2}}) \hat{j}$

$| \vec{R} |$ $= \sqrt{{(A + \frac{A}{\sqrt{2}})}^{2} + {(A - \frac{A}{\sqrt{2}})}^{2}} = \sqrt{3} A$

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Solution

Q. Three vectors OP→,OQ→ and OR→ each of magnitude A are acting as shown in figure. The resultant of the three vectors is Ax, The value of x is ______ . [2024]

Ans. (3) R→=(A+A2)i^+(A-A2)j^ |R→|=(A+A2)2+(A-A2)2=3A

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Q.
Three vectors $\vec{O P}, \vec{O Q}$ and $\vec{O R}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$ , The value of $x$ is ______ . [2024]

Ans.
(3)

$\vec{R} = (A + \frac{A}{\sqrt{2}}) \hat{i} + (A - \frac{A}{\sqrt{2}}) \hat{j}$

$| \vec{R} |$ $= \sqrt{{(A + \frac{A}{\sqrt{2}})}^{2} + {(A - \frac{A}{\sqrt{2}})}^{2}} = \sqrt{3} A$