Question

Find the direction cosine (l, m, n) of vector r = 3i -2j + 6k b. Given that p = -12 and q = 1. Find a unit vector u such that │u│= 35 and u is the direction of p-3q 5 -1

Answer 1

a.

$$\vec{r} = 3\vec{i} -2\vec{j} + 6\vec{k}$$

$$|\vec{r}|=\sqrt{(3)^2+(-2)^2+(6)^2}=7$$

$$(l, m, n)=(\dfrac{3}{7}, -\dfrac{2}{7}, \dfrac{6}{7})$$

b.

$$\vec{u} =\langle k(-12-3(1)), k(5-1)\rangle$$

$$\vec{u} =\langle-15k, 4k\rangle$$

$$|\vec{u}|=\sqrt{(-15k)^2+(4k)^2}=35$$

$$241k^2=35^2, k>0$$

$$k=\dfrac{35}{\sqrt{241}}$$

$$\vec{u} =\langle-\dfrac{525}{\sqrt{241}}, \dfrac{140}{\sqrt{241}}\rangle$$