If , and are three vectors such that and the angle between and is ,…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are three vectors such that

\mathbf{a} = \mathbf{b} + \mathbf{c}

and the angle between

\mathbf{b}

and

\mathbf{c}

\frac{\pi}{2}

, then (1)

a^2 = b^2 + c^2

(2)

b^2 = c^2 + a^2

(3)

c^2 = a^2 + b^2

(4)

2a^2 - b^2 = c^2

Related theory

Vector Operations
Vectors
Dot Product
Scalar product
Vector Algebra
Dot product of two vectors

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