Question

Сalculate whetger the vectors u and v are parallel, orthogonal or neither. u=langle5,3 rangle, u= langle frac{10}{4},- frac{3}{2} rangle

Polynomial arithmetic
ANSWERED
asked 2021-02-02
Сalculate whetger the vectors u and v are parallel, orthogonal or neither.
\(u=\langle5,3 \rangle, u= \langle \frac{10}{4},- \frac{3}{2} \rangle\)

Answers (1)

2021-02-03
Without finding the angle between two vectors, we can determine if they are parellel if they are scalar multiples of each other.
That is, if u = kv or v = ku for nonzero value of k since we are simply scaling. The two vectors are ort hogonal if thair dot product is \(0: u \cdot v = 0.\)
Check if they are parallel:
Since
\(v= -\frac{1}{2}u \rightarrow \langle-\frac{10}{4},-\frac{3}{2}\rangle = -\frac{1}{2}(5,3)\)
then u and v are parallel.
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