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