Question

ANSWER: (1)

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Answer 1

Answer:

(1)

Step-by-step explanation:

Let A be the angle between a and b.

Then cos A = (a.b) / |a||b| = 1 / 2 => A = π/3  ( or 60° ).

So sin A = √3/2, which means that

|a×b| = |a||b| sin A = (1)(2)(√3/2) = √3

=> 3a×b is orthogonal to b with length 3√3

=> c = 3a×b - b

goes horizontally (in the ab-plane) a distance -|b| = -2 and vertically 3√3.

The hypotenuse of this triangle (i.e. |c|) is then

√( 2² + (3√3)²) = √(4+27) = √31.

So the angle from b to c is

arccos ( horizontal measure / hypotenuse )

= arccos ( -2 / √31 )            ... and that is option (1)