Consider the vectors vec(u) = 2 vec(i) +vec(j) +vec(k) and vec(v) = vec(i) +2 vec(j) . a) Determine a positive orthornomal basis {vec(a) , vec(b) , vec(c) } with vec(a) parallel to vec(u) and vec(b) coplanar with vec(u) and vec(v) . b) Determine the coordinates of vec(w) = 3 vec(i) +4 vec(j) +5 vec(k) in the orthonormal basis { vec(a) , vec(b) , vec(c) }.

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

Find, correct to the nearest degree, the three angles of the triangle with the given vertices
A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

Whether f is a function from Z to R if 
a) ${\displaystyle f\left(n\right)=\pm n}$. 
b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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Find $\tan \left(22.5^{\circ }\right)$ using the half-angle formula.

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The solution set of $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=3\cot <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

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How do I find the value of sec(3pi/4)?