3. Vectors

Using the vectors given in the figure, (a) find A ● B. (b) Find A ● C.

Find the scalar product of the vectors A and B given in Exercise 1.38.

What is the angle Φ between vectors E and F in FIGURE P3.24?

(III) The arrangement of atoms in zinc is an example of 'hexagonal close-packed' structure. Three of the nearest neighbors are found at the following (x, y, z) coordinates, given in nanometers (10⁻⁹m) : atom 1 is at (0, 0, 0); atom 2 is at (0.230, 0.133, 0); atom 3 is at (0.077, 0.133, 0.247). Find the angle between two vectors: one that connects atom 1 with atom 2 and another that connects atom 1 with atom 3.

(II) Let V→ = 20.0î + 26.0ĵ - 14.0k̂ . What angles does this vector make with the x, y, and z axes?

Given the vectors $a=2.0i-4.0j+5.0k$ and $b=11.0i+2.5j$, what is the value of their dot product $a\cdot b$?

Given two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ that form an angle $\theta$ between them, which of the following correctly expresses the scalar (dot) product $\overrightarrow{a}\cdot \overrightarrow{b}$?