Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A√(x). The value of x is _________. Numerical answer type. Work it out, then open the answer.

Answer: 3. P (A)Q (A)R (A)O45°x-sum = A(1 + 1/√2)y-sum = A(1 − 1/√2) OP = Ai, OQ = Aj, OR = A/√(2)i - A/√(2)j Sum = A(1 + 1/√(2))i + A(1 - 1/√(2))j R² = A²[(1 + 1/√(2))² + (1 - 1/√(2))²] = A²(2 + 1) = 3A² R = A√(3), so x = 3.

Three vectors OP, OQ and OR each of magnitude A are acting as shown… | JEE Main 2024 (8 Apr, Shift 1)

Q11JEE Main 2024 · 8 APR · SHIFT 1Medium

Vector Basics, Unit Vectors & Components

Three vectors $\overrightarrow{OP}, \overrightarrow{OQ}$ and $\overrightarrow{OR}$ 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 _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

$\vec{OP} = A\hat{i}$ , $\vec{OQ} = A\hat{j}$ , $\vec{OR} = \frac{A}{\sqrt{2}}\hat{i} - \frac{A}{\sqrt{2}}\hat{j}$
Sum $= A\left(1 + \frac{1}{\sqrt{2}}\right)\hat{i} + A\left(1 - \frac{1}{\sqrt{2}}\right)\hat{j}$
$R^2 = A^2\left[\left(1 + \frac{1}{\sqrt{2}}\right)^2 + \left(1 - \frac{1}{\sqrt{2}}\right)^2\right] = A^2(2 + 1) = 3A^2$
$R = A\sqrt{3}$ , so $x = 3$ .

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