If $A = < - 1, 6, - 4 >$ $A= <-1 ,6 ,-4 >$ and $B = < 7, 2, 4 >$ $B= <7 ,2 ,4 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-12-15T07:10:49

The answer is $= - 71.5$ $=-71.5$

$\to A = ⟨ - 1, 6, - 4 ⟩$ $vecA=〈-1,6,-4〉$

$\to B = ⟨ 7, 2, 4 ⟩$ $vecB=〈7,2,4〉$

The dot product is $\to A . \to B = ⟨ - 1, 6, - 4 ⟩ . ⟨ 7, 2, 4 ⟩$ $vecA.vecB=〈-1,6,-4〉.〈7,2,4〉$

$= - 7 + 12 - 16 = - 11$ $=-7+12-16=-11$

The modulus of $\to A$ $vecA$ is $= ∥ \to A ∥ = ∥ ⟨ - 1, 6, - 4 ⟩ ∥ ∥ ∥$ $=∥vecA∥=∥〈-1,6,-4〉∥$

$= \sqrt{1 + 36 + 16} = \sqrt{53}$ $=sqrt(1+36+16)=sqrt53$

The modulus of $\to B$ $vecB$ is $= ∥ \to B ∥ = ∥ ⟨ 7, 2, 4 ⟩ ∥ ∥ ∥$ $=∥vecB∥=∥〈7,2,4〉∥$

$= \sqrt{49 + 4 + 16} = \sqrt{69}$ $=sqrt(49+4+16)=sqrt69$

Therefore,

$\to A . \to B - ∥ \to A ∥ \cdot ∥ \to B ∥ = - 11 - \sqrt{53} \cdot \sqrt{69}$ $vecA.vecB-∥vecA∥*∥vecB∥=-11-sqrt53*sqrt69$

$= - 11 - 60.5 = - 71.5$ $=-11-60.5=-71.5$

If A= <-1 ,6 ,-4 >A=<−1,6,−4>A= <-1 ,6 ,-4 > and B= <7 ,2 ,4 >B=<7,2,4>B= <7 ,2 ,4 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?