If $A = < - 3, 4, - 1 >$ $A= <-3 ,4 ,-1 >$ and $B = < 8, - 4, 2 >$ $B= <8 ,-4 ,2 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-11-09T15:22:52

The answer is $= (- 42 - \sqrt{2184})$ $=(-42-sqrt2184)$

The dot product is $\to A . \to B$ $vecA.vecB$
$= ⟨ - 3, 4, - 1 ⟩ . ⟨ 8, - 4, 2 ⟩ = - 24 - 16 - 2 = - 42$ $=〈-3,4,-1〉.〈8,-4,2〉=-24-16-2=-42$

The modulus of $\to A = ∥ \to A ∥ = \sqrt{9 + 16 + 1} = \sqrt{26}$ $vecA=∥vecA∥=sqrt(9+16+1)=sqrt26$

The modulus of $\to B = ∥ \to B ∥ = \sqrt{64 + 16 + 4} = \sqrt{84}$ $vecB=∥vecB∥=sqrt(64+16+4)=sqrt84$

$\to A . \to B - ∥ \to A ∥ ∥ \to B ∥ = - 42 - \sqrt{26 \cdot 84} = - 42 - \sqrt{2184}$ $vecA.vecB-∥vecA∥∥vecB∥=-42-sqrt(26*84)=-42-sqrt2184$

If A=<−3,4,−1>A= <-3 ,4 ,-1 > and B=<8,−4,2>B= <8 ,-4 ,2 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?