Answer:
the angle between the vectors [tex]\overrightarrow{a}[/tex] and [tex]\overrightarrow{b}[/tex] is [tex]cos\phi = \frac{1}{6}[/tex]
Step-by-step explanation:
Given -
[tex]|\overrightarrow{a}| = 4[/tex] , [tex]|\overrightarrow{b}| = 6[/tex] , [tex]|\overrightarrow{a} + \overrightarrow{b} | = 8[/tex]
If two vector [tex]\overrightarrow{a}[/tex] and [tex]\overrightarrow{b}[/tex] are inclined at an angle [tex]\phi[/tex]
vector parallelogram method
[tex]|\overrightarrow{a} + \overrightarrow{b} |^{2} = |\overrightarrow{a}|^{2} + |\overrightarrow{b}|^{2} + 2 |\overrightarrow{a}||\overrightarrow{b}|cos\phi[/tex]
64 = 16 + 36 + 48 [tex]cos\phi[/tex]
[tex]cos\phi = \frac{1}{6}[/tex]
