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More Vector Examples -

Ex. 5 Vector Product – Use the right hand rule; i.e. Calculate i x j . Result = k .

Ex. 6 Find the vector, F₃, perpendicular to the vectors, F₁ = 3i + 4j and

F₂ = 5i + 12j .

Solution:

Recall from vector calculus the cross product of two vectors is a vector perpendicular

to the original vectors.

F₁ x F₂ = ( 3i + 4j ) x [(5)i + (12)j]

Also recall that i x i = 0, j x j = 0, i x j = k, j x i = -k

So F₁ x F₂ = 36k - 48k = -12k

Ex. 7 Find the vector of F₁ = 3i + 4j in the direction of the vector, F₂ where

F₂ = 5i + 12j and where i and j are unit vectors in the x and y directions.

Solution:

From the first example the magnitude of the resulting vector in the direction of

vector, F₂ is 63/13 and the unit vector in the direction of F₂ is (5/13)i + (12/13)j .

The resulting vector, F₃, in the direction of F₂ is just its magnitude times the unit vector

in the direction of F₂ .

So F₃ = (63/13) [(5/13)i + (12/13)j] = (315/13)i + 756/13)j