**Question 1: **Find the length of the vector 7i + 2j + 6k.

** Solution: **

Let x = 7, y = 2, z = 6

Formula to find the length of the vector is $\sqrt{x^{2}+ y^{2}+ z^{2}}$

Plug in the values

$\sqrt{7^{2}+ 2^{2}+ 6^{2}}$ = 9.43

**Question 2: **Calculate the vector projection of $\vec{u}$ = 7$\vec{i}$ - 3$\vec{j}$ on the vector $\vec{v}$ = 6$\vec{i}$ + 6$\vec{j}$.

** Solution: **

$\vec{u}$ = 7$\vec{i}$ - 3$\vec{j}$ = 7(1, 0) - 3(0, 1)

= (7, 0) + (0, -3) = (7, -3)

$\vec{v}$ = 6$\vec{i}$ +6 $\vec{j}$ = 6(1, 0) + 6 (0, 1)

= (6, 0) + (0, 6) = (6, 6)

The formula to find vector projection is given by

proj$_{v}$ u = $\frac{\vec{u}.\vec{v}}{\vec{|v|}^{2}}$$\vec{v}$

$\frac{7.6 - 3.6}{36+36}$ (6, 6)

= $\frac{42 - 18}{72}$ (6, 6)

= ($\frac{144}{72}$, $\frac{144}{72}$)

= (2, 2)