If $A = < - 5, 3, - 7 >$ $A= <-5 ,3 ,-7 >$ and $B = < 2, - 9, 8 >$ $B= <2 ,-9 ,8 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-11-18T16:14:54

The answer is $= - 204.2$ $=-204.2$

We start by calculating the dot product.

$\to A . \to B = ⟨ - 5, 3, - 7 ⟩ ⟨ 2, - 9, 8 ⟩$ $vecA.vecB=〈-5,3,-7〉〈2,-9,8〉$

$= (- 5 \cdot 2) + (3 \cdot - 9) + (8 \cdot - 7)$ $=(-5*2)+(3*-9)+(8*-7)$

$= - 10 - 27 - 56 = - 93$ $=-10-27-56=-93$

Now, we calculate the modulus.

The modulus of $\to A = ∥ ⟨ - 5, 3, - 7 ⟩ ∥ = \sqrt{25 + 9 + 49}$ $vecA=∥〈-5,3,-7〉∥=sqrt(25+9+49)$

$= \sqrt{83}$ $=sqrt83$

The modulus of $\to B = ∥ ⟨ 2, - 9, 8 ⟩ ∥ = \sqrt{4 + 81 + 64}$ $vecB=∥〈2,-9,8〉∥= sqrt(4+81+64)$

$= \sqrt{149}$ $=sqrt149$

$\to A . \to B - ∥ \to A ∥ \cdot ∥ \to B ∥ = - 93 - \sqrt{83 \cdot 149} = - 204.2$ $vecA.vecB-∥vecA∥*∥vecB∥=-93-sqrt(83*149)=-204.2$

If A=<−5,3,−7>A= <-5 ,3 ,-7 > and B=<2,−9,8>B= <2 ,-9 ,8 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?