Light ray incident along a vector emerges out along vector as shown in the figure below. The value of C is

Question

Light ray incident along a vector $\vec{A O} (\vec{A O} = 2 \hat{i} - 3 \hat{j})$ emerges out along vector $\vec{O B} (\vec{O B} = C \hat{i} - 4 \hat{j})$ as shown in the figure below. The value of C is ______. [2026]

Smart Achievers · Accepted Answer

(1)

$1 (A O \times \hat{j}) \Rightarrow (O B \times \hat{j}) \times 1.5$

$\frac{2 \hat{k}}{\sqrt{13}} = \frac{3}{2} [\frac{C \hat{k}}{\sqrt{C^{2} + 16}}]$

$∴$ $\frac{4}{13} = \frac{9 C^{2}}{4 (C^{2} + 16)} \Rightarrow 16 C^{2} + 256 = 117 C^{2}$

$256 = 101 C^{2} \Rightarrow C = 1.59 \approx 1.6$

Solution

Q.
Light ray incident along a vector $\vec{A O} (\vec{A O} = 2 \hat{i} - 3 \hat{j})$ emerges out along vector $\vec{O B} (\vec{O B} = C \hat{i} - 4 \hat{j})$ as shown in the figure below. The value of C is ______. [2026]

1 1.6

2 0.16

3 11.6

4 16

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