Let , and be three vectors. A vector in the plane of and whose projection on is of…

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

Problem

Let

\mathbf{a} = 2\hat{\mathbf{i}} - \hat{\mathbf{j}} + \hat{\mathbf{k}}

\mathbf{b} = \hat{\mathbf{i}} + 2\hat{\mathbf{j}} - \hat{\mathbf{k}}

and

\mathbf{c} = \hat{\mathbf{i}} + \hat{\mathbf{j}} - 2\hat{\mathbf{k}}

be three vectors. A vector in the plane of

\mathbf{b}

and

\mathbf{c}

whose projection on

\mathbf{a}

is of magnitude

\sqrt{\frac{2}{3}}

is (1)

2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - 3\hat{\mathbf{k}}

(2)

2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} + 3\hat{\mathbf{k}}

(3)

-2\hat{\mathbf{i}} - \hat{\mathbf{j}} + 5\hat{\mathbf{k}}

(4)

2\hat{\mathbf{i}} + \hat{\mathbf{j}} + 5\hat{\mathbf{k}}

Related theory

Dot Product
Vectors
Vectors (Precalculus)
Scalar product
Vector Algebra
Projection of a vector on a line

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