find angle between A= 3i+4j and B=12i+5j

Asked by puneetgarg2555 | 27th May, 2018, 07:53: AM

Expert Answer:

The angle between the two vectors is given by,
 
cos space theta space equals space fraction numerator u with rightwards arrow on top. v with rightwards arrow on top over denominator open double vertical bar u with rightwards arrow on top. v with rightwards arrow on top close double vertical bar end fraction
L e t space stack u space with rightwards arrow on top space equals A with rightwards arrow on top space equals space 3 i with hat on top plus 4 j with hat on top
v with rightwards arrow on top equals space B with rightwards arrow on top equals 12 i with hat on top plus 5 j with hat on top
u with rightwards arrow on top. v with rightwards arrow on top equals space 3.12 space plus space 4.5 space equals 56
open double vertical bar u with rightwards arrow on top. v with rightwards arrow on top close double vertical bar space equals space square root of 3 squared plus 4 squared space end root space. space square root of 12 squared plus 5 squared space end root equals space 5 cross times 13 equals space 65 space
T h u s comma space cos space theta equals space 56 over 65 space equals space 56 over 65 equals space 0.86 space
T h u s comma space theta space equals space cos to the power of negative 1 end exponent left parenthesis 0.86 right parenthesis space equals space 30.5 to the power of omicron space
Thus, the angle between two vectors is 30.5°. 

Answered by Shiwani Sawant | 28th May, 2018, 12:04: PM