Question

The X-component of a vector of magnitude 8 is 4.
Find it's y-components :​

Answer 1

Explanation:

In the above figure, the components can be quickly read. The vector in the component form is v⃗ =⟨4,5⟩ .

The trigonometric ratios give the relation between magnitude of the vector and the components of the vector.

cosθ=Adjacent SideHypotenuse=vxv

sinθ=Opposite SideHypotenuse=vyv

vx=vcosθ

vy=vsinθ

Using the Pythagorean Theorem in the right triangle with lengths vx and vy :

| v |=vx2+vy2−−−−−−−√

Here, the numbers shown are the magnitudes of the vectors.

Answer 2

Explanation:

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The the standard form of a vector is xi + Yj

Its magnitude is √(x²+y²) =8

Squaring both the sides we get

x²+y²= 64

Given x=4

16+y²=64

y²=48

y=√48