Vectors V_1 and V_2 are different vectors with lengths V1 and V2 respectively.

UkusakazaL

UkusakazaL

Answered question

2021-06-04

Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the following:
a) V1V1 Express you answer in terms of V1
b) V1V2, when they are perpendicular
c) V1V2, when they are parallel

Answer & Explanation

davonliefI

davonliefI

Skilled2021-06-05Added 79 answers

Dot product of two vectors is equal to the magnitude of first vector multiplied by magnitude of second vector multiplied by the cosine angle between the two vectors.
AB=|A||B|cosθ
a) V1V1=|V1||V1|cos0
=(V1)(V1)
=V12
b) V1V2=|V1||V2|cosθ
If the two vectors are perpendicular to each other, then θ=90
Therefore,
V1V2=|V1||V2|cos90
=(V1)(V2)(0)
=0
d) V1V2=|V1||V2|cosθ
If the two vectors are parallel, the θ=0
Therefore
V1|V1||V2|cos0
=(V1)(V2)(1)
=V1V2

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