Question

the x and y components of a vector are 4√3 m and 4 m respectively. what angle does the vector makes with positive x-axis

Answer 1

x component = 4√3 î

y component = 4 j

So the vector = 4√3 î + 4 j

Magnitude = √((4√3)^2 + 4^2) = 8

And x-axis = 1 î

Therefore dot product = (4√3 î + 4 j)•(1 î + 0 j)

= (4√3)

And dot product is =

magnitude × cos (angle between vectors)

Therefore 4√3 =8 × cos (angle)

which implies cos (angle) = √3/2

Angle = 30° or 330° but since vector lies in 1st quadrant angle is 30°.

Good Luck!

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