If vector A = 2i +13j and B = 4i - 5j.
Calculate:
A) vector A - vector B and vector A + vector B
B) unit vector along vector A - vector B
A) To calculate vector A - vector B, we subtract the corresponding components of the vectors:
A - B = (2i + 13j) - (4i - 5j)
= 2i + 13j - 4i + 5j
= -2i + 18j
To calculate vector A + vector B, we add the corresponding components of the vectors:
A + B = (2i + 13j) + (4i - 5j)
= 2i + 13j + 4i - 5j
= 6i + 8j
B) To find the unit vector along vector A - vector B, we divide the vector A - B by its magnitude.
Magnitude of A - B = sqrt((-2)^2 + (18)^2) = sqrt(4 + 324) = sqrt(328)
Unit vector along A - B = (A - B) / |A - B|
= (-2i + 18j) / sqrt(328)
= (-2/sqrt(328))i + (18/sqrt(328))j