Let , and be the vertices of a triangle whose position vectors with respect to an…

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let

A

B

and

C

be the vertices of a triangle whose position vectors with respect to an origin

O

are

\mathbf{a}=2\mathbf{i}+3\mathbf{j}+\mathbf{k}

\mathbf{b}=-\mathbf{i}+4\mathbf{j}+2\mathbf{k}

and

\mathbf{c}=5\mathbf{i}-\mathbf{j}+3\mathbf{k}

respectively. (i) Find the length of the altitude drawn from vertex

A

to side

BC

. (ii) Obtain, in vector form, the position vector of the foot

D

of this altitude.