Question

Study the vector diagram.

Three vectors are drawn tail to tip method in the x y plane. Vector labeled T starts at the origin and is drawn in the northeast direction. The second vector is labeled U and drawn in the south south east direction. The third is labeled V and drawn in the north northeast direction. X and Y components are drawn for each vector along the x and y axis.

Which formula can be used to find the x-component of the resultant vector?
Tx - Ux - Vx
Tx + Ux + Vx
Tx = Tcosθ
Tx = Tsinθ

Answer 1

The formula that can be used to find the x-component of the resultant vector is
`\(Tx = T \cos \theta\)`.

To find the x-component of the resultant vector in a vector diagram, you use the formula
`\(Tx = T \cos \theta\)`. This formula involves the magnitude of the vector T and the cosine of the angle
`\(\theta\)` between vector T and the x-axis.

The x-component (
`\(Tx\)`) represents the projection of the vector T onto the x-axis. It is determined by multiplying the magnitude of the vector (T) by the cosine of the angle
`\(\theta\).`

This mathematical relationship is derived from trigonometry and is applicable when the vector components are expressed in a coordinate system.

Utilizing this formula allows for the efficient determination of the x-component, providing essential information about the horizontal component of the vector's magnitude in the x-y plane.