Question

# Write the vector v in the form ai + bj, given its magnitude ∥v∥∥v∥ and the angle alpha it makes with the positive x-axis. ∥v∥=8,alpha=45*∥v∥=8,alpha=45

Vectors and spaces

Write the vector v in the form ai + bj, given its magnitude ∥v∥∥v∥ and the angle $$\alpha$$ it makes with the positive x-axis. $$∥v∥=8,\alpha=45*∥v∥=8,\alpha=45$$

||v||=8 & $$a+45^{\circ}=>a=8\cos45^{\circ}=8*\sqrt{2/2}$$
$$=4\sqrt{2}$$ &
$$b= 8\sin45^{\circ}=8*\sqrt{2}/2=4\sqrt{2}=>$$
$$v=4\sqrt{2i}+4\sqrt{2j}$$