Find the resultant and the direction of resultant of two vectors A and B with angle straight theta between them

Asked by neerajchauhan000000 | 23rd Sep, 2021, 03:33: PM

Expert Answer:

Figure shows two vectors a and b . Let θ be the angle between vectors.
By law of parallelogram, resultant vector (a+b) is the diagaonal of the parallelogram
formed by the vectors a and b as sides as shown in figure.
 
Magnitude of resultant (a+b) is determined using law of cosines using the triangle
formed by vector a , vector b and the resultant (a+b)
 
begin mathsize 14px style open vertical bar a plus b close vertical bar space equals space square root of open vertical bar a close vertical bar squared plus open vertical bar b close vertical bar squared space minus space 2 space open vertical bar a close vertical bar space open vertical bar b close vertical bar space cos left parenthesis 180 minus theta right parenthesis end root end style
begin mathsize 14px style open vertical bar a plus b close vertical bar space equals space square root of open vertical bar a close vertical bar squared plus open vertical bar b close vertical bar squared space plus space 2 space open vertical bar a close vertical bar space open vertical bar b close vertical bar space cos theta end root end style
 
 

Answered by Thiyagarajan K | 24th Sep, 2021, 12:55: AM