Question

I can find out if a vector is orthogonal by solving the dot product and is equal to zero. If the question asks: determine whether the vector is orthogonal, parallel, or neither; how can I find out if it is parallel or neither? Vector a = <-5,3,7>, Vecor b = <6,-8,2>

Answer 1

Multiply the length of a times the length of b. If this is equal to the dot product, the vectors are parallel. If the dot product is 0, they are orthogonal. Otherwise, they are neither parallel or orthogonal.

Answer 2

The first trick works because \[\vec a\cdot \vec b=||\vec a|| \;\;||\vec b||\;\;\cos(\theta)\]If they're parallel \(\cos(\theta)=\pm 1\). So technically, the length of a times the length of b could also be -1 times the dot product.

Answer 3

for parallel, i set up a ratio of compontents; a/b or b/a, doesnt matter

and if they form a set of equal ratios, or porportions they are parallel

Answer 4

a = <-5,3,7>
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b = <6,-8,2>

-5/6 not= -3/8 not= 7/2 ... not paralell