Question

Let a and b be vectors such that lal =3.75 , lbl= 2.93 and, (a,b)= 71.5 . Calculate
la+bl and la- bl . Can anyone help please?

Answer 1

the magnitude squared
\[ |a+b| ^2 = (a+b) \cdot (a+b) \]
by the distributive property of the dot product
\[ = a\cdot(a+b) + b\cdot (a+b) = a \cdot a + a \cdot b + b \cdot a + b \cdot b\]
or
\[ = |a|^2 + 2 (a \cdot b) + |b|^2 \]
you know each of those terms from the given in the problem
now take the square root to find | a+b |

use the same idea for | a -b |

Answer 2

I used the law of cosines and I got \[\left| a+b \right|\]\[^{2}\]=|a| 2 -2(a⋅b)+|b| 2 .. Is it right to used the law of cosines here?

Answer 3

you do not know the angle A, but I think with work you can figure it out.
It is easier to just replace |a|^2 with the number they gave you 3.75^2
do the same for |b| and (a,b) in
\[ |a|^2 + 2 (a \cdot b) + |b|^2 \]