# Thread: given that vector v1=2i-3j & v2=i+5j find:

1. ## given that vector v1=2i-3j & v2=i+5j find:

a) the magnitude of the vector v1+(2xv2)
b) the unit vector in the direction of (2xv1)-v2

2. ## Re: given that vector v1=2i-3j & v2=i+5j find:

Originally Posted by bobmarly12345
a) the magnitude of the vector v1+(2xv2)
b) the unit vector in the direction of (2xv1)-v2
To a):

$\displaystyle \overrightarrow{v_1} = \langle 2,-3 \rangle$

$\displaystyle \overrightarrow{v_2} = \langle 1,5 \rangle$

then $\displaystyle \overrightarrow{v_1} + 2 \cdot \overrightarrow{v_2} = \langle 2,-3 \rangle + 2 \cdot \langle 1,5 \rangle$

Continue.

To b)

Determine

$\displaystyle 2 \cdot \overrightarrow{v_1} - \overrightarrow{v_2}$

Determine the length (the absolute value) of this vector sum. (I've got $\displaystyle |2\cdot \overrightarrow{v_1} - \overrightarrow{v_2} | = \sqrt{130}$ )

Let $\displaystyle \vec u$ denote a unit vector in the direction of $\displaystyle \vec v$. Then this unit vector is determined by: $\displaystyle \vec u = \frac{\vec v}{|\vec v|}$