Three displacement vectors in space are given by , , .

PHYSICS · Multi-part · AP · Physics C: Mechanics · Kinematics · Kinematics

Problem

Three displacement vectors in space are given by

\vec A = 3\,\hat i - 2\,\hat j + 6\,\hat k\,\text{m}

\vec B = -5\,\hat i + 4\,\hat j + 2\,\hat k\,\text{m}

\vec C = 4\,\hat i + 3\,\hat j - 8\,\hat k\,\text{m}

. (i) Obtain the rectangular components of the resultant displacement

\vec R = \vec A + \vec B + \vec C

. (ii) Compute the magnitude of

\vec R

. (iii) Determine the direction cosines of

\vec R

and hence find the angles that

\vec R

makes with the positive

x

–,

y

– and

z

–axes, giving each angle to the nearest degree.