Let r⃗=(a⃗×b⃗)sin⁡x+(b⃗×c⃗)cos⁡y+(c⃗×a⃗)\vec{r} = (\vec{a} \times \vec{b}) \sin x + (\vec{b} \times \vec{c}) \cos y + (\vec{c} \times \vec{a})…

Mathematics

Problem

Let r⃗=(a⃗×b⃗)sin⁡x+(b⃗×c⃗)cos⁡y+(c⃗×a⃗)\vec{r} = (\vec{a} \times \vec{b}) \sin x + (\vec{b} \times \vec{c}) \cos y + (\vec{c} \times \vec{a}) , where a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c} are non-zero non-coplanar vectors. If r⃗\vec{r} is orthogonal to 3a⃗+5b⃗+2c⃗3\vec{a} + 5\vec{b} + 2\vec{c} , then the value of sec⁡2y+csc⁡2x+sec⁡ycsc⁡x\sec^2 y + \csc^2 x + \sec y \csc x is a. 3 b. 4 c. 5 d. 6

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