Vectors v and w are given in magnitude and direction form. find the coordinate representation of the sum v + w
and the difference v − w. give coordinates to the nearest tenth of a unit.
a. v: magnitude 12, direction 50° east of north
w: magnitude 8, direction 30° north of east
b. v: magnitude 20, direction 54° south of east
w: magnitude 30, direction 18° west of south

a) v + w = 13.2 i + 14.6 j

v - w = 5.2 i + 0.8 j

b) v + w = 2.5 i - 44.7 i

v - w = 21 i + 12.4 i

Step-by-step explanation:

a) For v:  ∡ = 90º-50º = 40º

v = 12*cos 40º i + 12*Sin40º j

For w:  ∡ = 90º-30º = 60º

w = 8*Cos 60º i + 8*Sin 60º j

v + w = (12*cos 40º+8*Cos 60º) i + (12*Sin40º+8*Sin 60º) j

v + w = 13.2 i + 14.6 j

v - w = (12*cos 40º-8*Cos 60º) i + (12*Sin40º-8*Sin 60º) j

v - w = 5.2 i + 0.8 j

b) For v:  ∡ = -54º (clockwise)  

v = 20*cos (-54º) i + 20*Sin(-54º) j

For w:  ∡ = 270º-18º = 252º

w = 30*Cos 252º i + 30*Sin 252º j

v + w = (20*cos (-54º)+30*Cos 252º) i + (20*Sin(-54º)+30*Sin 252º) j

v + w = 2.5 i - 44.7 i

v - w = (20*cos (-54º)-30*Cos 252º) i + (20*Sin(-54º)-30*Sin 252º) j

v - w = 21 i + 12.4 i

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

3100

step-by-step explanation: