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)
Vector A - vector B = (2i + 13j) - (4i - 5j)
= 2i + 13j - 4i + 5j
= -2i + 18j
Vector A + vector B = (2i + 13j) + (4i - 5j)
= 2i + 13j + 4i - 5j
= 6i + 8j
B)
To find the unit vector along the vector A - vector B, first we need to find the magnitude of vector A - vector B:
Magnitude of vector A - vector B = √((-2)^2 + 18^2)
= √(4 + 324)
= √328
= 18.14 (approx)
Now, the unit vector along vector A - vector B is:
= (-2i + 18j)/18.14
= -0.11i + 0.99j