Two nonzero vectors are parallel if they point in the same direction o

goymdujf

goymdujf

Answered question

2021-11-12

Two nonzero vectors are parallel if they point in the same direction or in opposite directions. This means that if two vectors are parallel, one must be a scalar multiple of the other. Determine whether the given vectors u and v are parallel. If they are, express v as a scalar multiple of u.

Answer & Explanation

George Blue

George Blue

Beginner2021-11-13Added 18 answers

If two vector u and v are parallel then we can represent vector u as scalar multiple of vector u that means v=λu where λ is scalar
a) Here given vector u=<3,2,4> and v=<6,4,8>
v=<6,4,82<3,2,4>
v=2u - vector v is scalar multiple of vector u So given two vectors are parallel
b) Here given vector u=<9,6,12> and v=<12,8,16>
u=<9,6,123<3,2,4>
13u=<3,2,4>
v=<12,8,164<3,2,4>
v=<12,8,16413u
v=43u vector v is scalar multiple of vector u So given two vectors are parallel
c) Here given vector u=i+j+k and v=2i+2j2k
Here the two vectors cannot be represented by scalar multuiple. So the vectors are not parallel.

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