What are the properties of two vectors `vecA` and `vecB` such that:
(a) `vecA + vecB = C and A + B =C `
(b) `vecA + vecB =vecC and A^(2) + B^(2) = C^(2)`

Answer

(a) paralle ( `theta = 0^(@)`), (b) perpendicular (`theta= 90^(@)`)

Explanation

(a) `vecA + vecB =vecC`
For parallel vectors i.e., (a) `vecA + vecB =vecC`
`|vecC| = sqrt(A^(2) + B^(2) + 2AB cos theta)`
`C = sqrt(A^(2) + B^(2) + 2AB cos theta)`
`C = sqrt((A^(2) + B^(2)))`
`C = A+ B `
`i.e.," "A + B =C`
(b) `vecA + vecB = vecC`
For perpendicular vectors `i.e., theta= 90^(@)`
`|vecC| = sqrt(A^(2) + B^(2) + 2AB cos 90^(@))`
`C = sqrt(A^(2)+ B^(2))`
`C^(2) = A^(2) + B^(2)`
`A^(2) + B^(2) = C^(2)`