Dot Product

Algebra Level 3

If A ⃗ \vec { A } and B ⃗ \vec { B } are two perpendicular unit vectors , then what is ( A ⃗ − 2 B ⃗ ) ⋅ ( 3 A ⃗ + 5 B ⃗ ) (\vec { A } -2\vec { B } ) \cdot (3\vec { A } +5\vec { B } ) ?

-7 -8 24 0

Rawan Medhat by Rawan Medhat , 22, Egypt

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1 solution

Anthony Holm
Sep 14, 2016

The dot product is defined as the sum of the coordinate-wise products of the two vectors. With this coordinate system that means take the product of the two A components and add the product of the two B components. Specifically, (1)(3)+(-2)(5)=-7

0 Helpful 0 Interesting 0 Brilliant 0 Confused

But we also consider the cosine of angle between the vectors in case of dot product. And the angle between the vectors is given as 90° ,cos 90°=0.

Nashita Rahman - 4 years, 9 months ago

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