यदि `vecA = 4 hati - 3 hatj ` और `vec B = 6 hati + 8 hatj` है, तो `vecA + vecB` का परिमाण और दिशा क्या होगी?

Options

A. `5, tan ^(-1) ""((3)/(4))`
B. `5 sqrt5 , tan ^(-1) "" ((1)/(2))`
C. `10, tan^(-1) (5)`
D. `25, tan ^(-1) "" ((3)/(4))`

Answer

B

Explanation

`vecA + vec B = (4 hati - 3 hatj ) + ( 6 hati + 8 hatj ) = 10 hati +5 hatj `
`|vecA + vecB| = sqrt ((10 ) ^(2) + (5) ^(2)) = 5 sqrt5`
`tan theta = (5)/(10) = (1)/(2)`
`implies theta = tan ^(-1) ((1)/(2))`