Question

Find the angle between v and w. v= - 31+ 8j, w= w=3i+9j The angle between v and wis (Do not round until the final answer. Then round to the nearest tenth as needed.) Enter your answer in the answer box

Answer 1

Solution-

The angle between two vectors a and b is given by

cos(0) ab |al|6

Now,

For vector v = -3i +8j and w = 3i +9j

The dot product is

v•w = (-3i +8j)•(3i +9j) = (-3)×(3) + (8)(9) = -9 +72 = 63

And

Magnitude of vectors are

$|v|=\sqrt{(-3)^2+(8)^2} = \sqrt{9 +64}=\sqrt{73}$

$|w|=\sqrt{(3)^2+(9)^2} = \sqrt{9 +81}=\sqrt{90}=3\sqrt{10}$

Now, the angle between vectors v and w is given by

cos(6)

$cos(\theta)=\frac{63}{(\sqrt{73})(3\sqrt{10})}$

$cos(\theta)=0.7772448707$

$\theta=cos^{-1}(0.7772448707)$

$\theta=38.99^o$

$\theta=39. 0^o$

Hence, the angle between v and w is 39.0° .