Question

For vectors →B=−4ˆx−7ˆyB→=-4x^-7y^ and →A=−5ˆx−2ˆyA→=-5x^-2y^ calculate:

1. →A+→B=A→+B→=   ˆx+x^+   ˆyy^
   
   ∣∣→A+→B∣∣=|A→+B→|= (round to one decimal place)
   Direction in degrees relative to +x−+x- axis: (round to one decimal place)
2. →A−→B=A→-B→=   ˆx+x^+ ˆyy^
     
   ∣∣→A−→B∣∣=|A→-B→|= (round to one decimal place)
   Direction in degrees relative to +x−+x- axis: (round to one decimal place)

Answer 1

a )

given

A = - 5x - 2y

B = - 4x - 7y

A + B = ( - 5x - 2y ) +( - 4x - 7y )

= - 9 x - 9 y

| A + B | = 9x + 9y

|| A + B || = ( 9² + 9² )^1/2

= 12.727 units

direction in degrees is $\theta$ = tan^-1 ( 9/9 )

$\theta$ = 45^o

b )

given

A = - 5x - 2y

B = - 4x - 7y

A - B = ( - 5x - 2y ) - ( - 4x - 7y )

= ( - 5x - 2y + 4x + 7y )

= - x + 5y

| A - B | = x - 5y

|| A - B || = ( 1² + (-5² ) )^1/2

= 5.099 units

direction in degrees is $\theta$ = tan^-1 ( -5/1 )

$\theta$ = - 78.69^o