Question

Write t with magnitude 14 and direction 51 degrees in component form

Answer 1

(14cos51, 14sin51)

8.81 i, 10.88 j

Answer 2

The component form of the vector with magnitude 14 and direction angle 51 will be (8.810, 10.880).

What is Component Form of a Vector?

The component form of a vector describes a vector that has gone x units to the left and y units to the right of the origin.

How to solve this problem?

Here, we have direction angle θ=51°  and magnitude V= 14

∴ x-component will be given by-

$v_{x}$ = V* cos(θ)

   = 14* cos(51°)

   = 14* 0.629

   = 8.810

and y-component will be given by-

$v_{y}$ = V* sin(θ)

   = 14* sin(51°)

   = 14* 0.777

   = 10.880

Therefore, the component form of the vector is (8.810, 10.880)

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