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anonymous
 one year ago
Find a • b.
a = 4i + 8j, b = 2i + 3j
anonymous
 one year ago
Find a • b. a = 4i + 8j, b = 2i + 3j

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.1this is the 'dot' product of 2 vectors a . b = 4i*2i + 8j*3j

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1its also called the Scalar product

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1can you simplify this further?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1the square of the unit vectors i and j both = 1

Empty
 one year ago
Best ResponseYou've already chosen the best response.2@xamr Almost, but the dot product gives you a single value not a pair of values. So you need to ad those two numbers together. One application of the dot product is to calculate length which is the square root of the dot product, $$\text{length of vector a} = \sqrt{\vec a \cdot \vec a }$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By thinking of i,j,k as components x,y,z we can rewrite vectors a and b. \[\vec a = \langle 4~,~8\rangle ~,~ \vec b = \langle 2~,~ 3\rangle\]

Empty
 one year ago
Best ResponseYou've already chosen the best response.2when you dot a vector with another vector, you get the amount of projection of one vector onto another. So if two vectors are at right angles to each other, then there's no projection at all, and the dot product is zero $$\vec a \cdot \vec b = 0 $$ means they're perpendicular to each other
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