If $A = < 3, 1, - 4 >$ $A= <3 ,1 ,-4 >$ and $B = < 4, - 7, 3 >$ $B= <4 ,-7 ,3 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-12-27T11:17:01

The answer is $= - 50.9$ $=-50.9$

The dot product is $\to A . \to B$ $vecA.vecB$

$= ⟨ 3, 1, - 4 ⟩ . ⟨ 4, - 7, 3 ⟩$ $=〈3,1,-4〉.〈4,-7,3〉$

$= (3 \cdot 4 - 1 \cdot 7 - 4 \cdot 3)$ $=(3*4-1*7-4*3)$

$= 12 - 7 - 12 = - 7$ $=12-7-12=-7$

The modulus of $\to A$ $vecA$ is $= ∥ \to A ∥ = ∥ ⟨ 3, 1, - 4 ⟩ ∥ ∥ ∥$ $=∥vecA∥=∥〈3,1,-4〉∥$

$= \sqrt{9 + 1 + 16} = \sqrt{26}$ $=sqrt(9+1+16)=sqrt26$

The modulus of $\to B$ $vecB$ is $= ∥ \to B ∥ = ∥ ⟨ 4, - 7, 3 ⟩ ∥ ∥ ∥$ $=∥vecB∥=∥〈4,-7,3〉∥$

$= \sqrt{16 + 49 + 9} = \sqrt{74}$ $=sqrt(16+49+9)=sqrt74$

Therefore,

$\to A . \to B - ∥ \to A ∥ \cdot ∥ \to B ∥ ∥ ∥$ $vecA.vecB-∥vecA∥*∥vecB∥$

$= - 7 - \sqrt{26 \cdot 74}$ $=-7-sqrt(26*74)$

$= - 7 - 43.9 = - 50.9$ $=-7-43.9=-50.9$

If A= <3 ,1 ,-4 >A=<3,1,−4>A= <3 ,1 ,-4 > and B= <4 ,-7 ,3 >B=<4,−7,3>B= <4 ,-7 ,3 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?