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-BARSIC- [3]
3 years ago
13

Find the component form of the vector v ⃗ with ‖v ⃗ ‖=4√3 when drawn in standard position v ⃗ lies in Quadrant II and makes a 30

° angle with the positive y-axis. Give exact values.
Mathematics
1 answer:
nydimaria [60]3 years ago
8 0
The answer:

first of all, we should know that the expression of a vector V (a, b) can be written as follow:

V = r (Vx i + Vyj), where r is the length of the vector, it is r = sqrt(V²x + V²y)
Vx is the component lying on the x-axis and Vy on the y-axis

<span>v ⃗ lies in Quadrant II, means Vx is less than 0 (negative)
</span>
so Vx= -r sin30° and Vy= rcos30° 

r= <span>‖v ⃗ ‖=4√3 
</span>
so we have   v = - 4√3sin30° i  + 4√3 cos30° j

the components are 

v(- 4√3sin30°,  4√3 cos30°) = (-2√3, 4√3 cos30°)
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