Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §11.1 Vectors and Dot Products, #16 · Multivariable Calculus · Vectors & geometry

(a) Draw the unit vectors … and

(a) Draw the unit vectors $u_{1} = (cos θ, sin θ)$ and $u_{2} = (cos ϕ, sin ϕ)$ . By dot products find the formula for $cos (θ - ϕ)$ .
(b) Draw the unit vector $u_{3}$ from a $9 0^{\circ}$ rotation of $u_{2}$ . By dot products find the formula for $sin (θ + ϕ)$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.1 Vectors and Dot Products, #16

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