To find (a), the component of vector A along the direction of vector B, we can use the dot product formula:
(a) = (A * B) / |B| * B
where A and B are the given vectors, * represents the dot product, and |B| represents the magnitude (length) of vector B.
To find (b), the component of vector B along the direction of vector A, we can use the same formula:
(b) = (B * A) / |A| * A
To find (c), the projection of A onto B, we can use the formula
(c) = (A.B/|B|^2) * B
To find (d), the projection of B onto A, we can use the formula
(d) = (B.A/|A|^2) * A
It's worth noting that the above calculation requires the vectors to be in the same dimension and unit, and the dot product and magnitude calculations should be done accordingly.
