Length of a vector
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The length of a vector is defined as
- ∣∣(x1,x2,…,xn)∣∣=x12+x22+⋯+xn2
The dot product
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What is the Dot product
- let u=(u1,u2,…,un) and v=(v1,v2,…,vn) be two vectors in Rn the dot product of u,v is defined as
- u⋅v=u1v1,u2v2+⋯+unvn
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Loosly, the dot product is a measure of how much one vector is “towards the directon” or the otheroq
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If two vectors dot product is 0 they are orthogonal
- u∗v=0 they are perpendicular
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EX
- finding all vectors v that are orthoganal to both (1,0,2),and(1,2,3)
a+0b+2c=0a+2b+3c=0⟹[11022300]→RREF[100121/200]∴a=−2t,b=−21b
angles between two vectors