I have two high dimensional unit vectors vec(a) and vec(b) and the distance d between them. I want to change the vector vec(a) so that it is still a unit vector but the distance to vec(b) is now d′ . I already tried it this way: vec(a)′=vec(a) +(vec(b) −vec(a) *(1−(d′)/(d))) But then the new vector does not have unit length.

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
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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

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