If the vector A= 6m and B= 8m magnitude are joined tail to tail. Find the magnitude of sum of vectors.
To find the magnitude of the sum of vectors A and B when joined tail to tail, we can use the parallelogram rule of vector addition.
The magnitude of the sum of vectors A and B can be found using the formula:
|A + B| = sqrt((A^2 + B^2 + 2ABcosθ))
Where:
A = magnitude of vector A = 6m
B = magnitude of vector B = 8m
θ = angle between vectors A and B (180 degrees since they are joined tail to tail)
Plugging in the values, we get:
|A + B| = sqrt((6^2 + 8^2 + 2(6)(8)cos(180)))
|A + B| = sqrt(36 + 64 + 96(-1))
|A + B| = sqrt(36 + 64 - 96)
|A + B| = sqrt(4)
|A + B| = 2m
Therefore, the magnitude of the sum of vectors A and B when joined tail to tail is 2m.