MATH SOLVE

7 months ago

Q:
# Vector v1 is 6.6 units long and points along the negative x axis. vector v2 is 8.5 units long and points at + 55° to the positive x axis. (a) what are the x and y components of each vector? (b) determine the sum v v 1 2

Accepted Solution

A:

(a) what are the x and y components of each vector?

For vector v1:

v1 = 6.6 (cos (180) i + sine (180) j)

v1 = 6.6 (-1i + 0j)

v1 = -6.6i

For vector v2:

v2 = 8.5 (cos (55) i + sine (55) j)

v2 = 8.5 ((0.573576436) i + (0.819152044) j)

v2 = 4.88 i + 6.96 j

(b) determine the sum v v 1 2

The sum of both vectors is given by:

v1 + v2 = (-6.6i) + (4.88 i + 6.96 j)

Adding component to component:

v1 + v2 = (-6.6 + 4.88) i + (6.96) j

v1 + v2 = (-1.72) i + (6.96) j

For vector v1:

v1 = 6.6 (cos (180) i + sine (180) j)

v1 = 6.6 (-1i + 0j)

v1 = -6.6i

For vector v2:

v2 = 8.5 (cos (55) i + sine (55) j)

v2 = 8.5 ((0.573576436) i + (0.819152044) j)

v2 = 4.88 i + 6.96 j

(b) determine the sum v v 1 2

The sum of both vectors is given by:

v1 + v2 = (-6.6i) + (4.88 i + 6.96 j)

Adding component to component:

v1 + v2 = (-6.6 + 4.88) i + (6.96) j

v1 + v2 = (-1.72) i + (6.96) j