Question

Find the angle between U =4i - 2j + 4k and V = 3i - 6j - 2k .

680
670
580
690

Answer 1

Answer on Question #46886 – Math – Vector Calculus

Question:

Find the angle between U = 4i - 2j + 4k and V = 3i - 6j - 2k.

680

670

580

690

Solution:

The angle between two vectors is given by the formula:

$$\cos \theta = \frac {\vec {u} \cdot \vec {v}}{| \vec {u} | \cdot | \vec {v} |}$$

where $\vec{u} \cdot \vec{v}$ is dot product, $|\vec{u}|$ is length of vector.

Therefore:

$$\cos \theta = \frac {4 \cdot 3 + (- 2) (- 6) + 4 (- 2)}{\sqrt {4 ^ {2} + (- 2) ^ {2} + 4 ^ {2}} \sqrt {3 ^ {2} + (- 6) ^ {2} + (- 2) ^ {2}}} = \frac {1 6}{7 \sqrt {2 9}} \cong 0. 3 8$$

Or:

$$\theta = \arccos 0. 4 2 4 = 6 7. 6 {}^ {\circ} \cong 6 8 {}^ {\circ}$$

Answer: $68{}^{\circ}$

www.AssignmentExpert.com