Will someone please answer these Pre Calculus questions?

Question

IT"S URGENT!

Which of the following represents vector w  = ⟨-10, -24⟩ in trigonometric form?

A. w = 26(cos 67.38°i + sin 67.38°j)

B. w = 26(cos 247.38°i + sin 247.38°j)

C. w = 61(cos 190.39°i + sin 190.39°j)

D. w = 61(cos 10.39°i + sin 10.39°j)

Vectors u = −10i - 3j and v = 7i − 6j. What is 2u + 5v?

A. 15i − 36j

B. − 17i − 6j

C. − 55i − 39j

D. 15i - 51j

Given vector u = 30 ⟨cos 60°, sin 60°⟩, what are the magnitude and direction of −6u?

A. 210; 60°

B. 210; 240°

C. 180; 240°

D. -180; 60°

A vector has a magnitude of 35 and a direction of 55° while a second vector has a magnitude of 80 and a direction of 100°. What are the magnitude and direction of their resultant? 

A. 107.633; 87°

B. 84.315; 289°

C. 95.260; 109°

D. 89.954; -71°

Answer 1

26(cos247.38, sin247.38)

= the point (-10,-24)

hypotenuse = 26= sqr(10^2+24^2) = sqr676 = 26

reference angle =67.38= tan^-1(24/10)

add 180 to get 247.38

2u+5v

=(-20+35)i -6-30

=16i-36

vector has magnitude 35, direction 55 degrees

2nd vector has magnitude 80, direction 100 degrees

resultant vector has diagonal length of a parallelogram contructed with angles 45 degrees and 135 degrees

use the law of cosines

d^2 = 35^2 + 80^2 -2(35)(80)Cos135

= 1225+ 6400 -5600Cos135

= 7625 +5600Cos45

= 7625+5600sqr2/2

=7625 +2800sqr2

= about 7625 +2800(1.414)

=about 7625 +3959.8

= 11644.2

d=sqr11644.2

= about 107.9

direction is somewhere between 100 and 55 degrees

to find the direction, use the law of sines

sin135/107.9= sinA/80 A +55 = the direction

sinA= 80sin135/107.9 =80sin45/107.9

=about 80(.707)/107.9=.524

A= sin^-1(.524)

A= 31.62

A+55 = 86.62 degrees

Answer A) looks good