# if |a|=3, |b|=4 and the angle between be 120 degree, then |4a + 3b|=?

Sujit Kumar
111 Points
4 years ago
Magnitude of vector a = 3
Magnitude of vector b = 4

magnitude of vector 4a = 12
magnitude of vector 3b = 12

angle between vector a & vector b = 120
angle between vector 4a & vector 3b = 120

$Magnitude\ of\ 4a+3b=|4a+3b|=[(4a)^{2}+(3b)^{2}+2(4a)(3b)cos120]^{\frac{1}{2}}$
$\rightarrow |4a+3b|=[(12)^{2}+(12)^{2}-2(12)(12)cos60]^{\frac{1}{2}}$
$\rightarrow |4a+3b|=[(12)^{2}+(12)^{2}-2(12)^{2}\frac{1}{2}]^{\frac{1}{2}}$
$\rightarrow |4a+3b|=[(12)^{2}]^{\frac{1}{2}}$
$\rightarrow |4a+3b|=12$

Ans: 12