|a| = 5, and b = 8, and the angle formed by a and b is 55°. Determine |4a + b|. Round
your answer to 2 d.p.
Draw the diagram. Using the law of cosines, if c = 4a+b, then
|c|^2 = 20^2 + 8^2 - 2*8*20 cos125°
To determine |4a + b|, we need to find the magnitude (or absolute value) of the vector 4a + b.
First, let's find the vector 4a by multiplying vector a by 4:
4a = 4 * |a|
= 4 * 5
= 20
Next, let's add vector 4a and vector b:
4a + b = 20 + 8
= 28
Now, let's find the magnitude of the vector 4a + b:
|4a + b| = √((4a + b)^2)
= √(28^2)
= √784
= 28
Therefore, |4a + b| = 28.