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------------------------------------------------ Find the component form for the vector **v** with the given magnitude and direction angle [tex]\theta[/tex].

Magnitude: [tex]99.9[/tex], [tex]\theta = 68.6^\circ[/tex]

Answer :

The component form of the vector v is < 99.9 cos(68.6°), 99.9 sin(68.6°) >

To find the component form of the vector v, we need to use the magnitude and direction angle provided.

The magnitude of the vector v is given as 99.9. This represents the length or size of the vector.

The direction angle, θ, is given as 68.6°. This angle represents the direction in which the vector is pointing.

In the component form of a vector, the first component represents the magnitude of the vector in the x-direction, and the second component represents the magnitude in the y-direction.

To find the x-component of the vector, we use the formula: magnitude * cos(angle). Substituting the given values, we have: 99.9 * cos(68.6°).

To find the y-component of the vector, we use the formula: magnitude * sin(angle). Substituting the given values, we have: 99.9 * sin(68.6°).

Therefore, the component form of the vector v is < 99.9 cos(68.6°), 99.9 sin(68.6°) >.

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