If $A = < 8, - 2, 9 >$ $A= <8 ,- 2 ,9>$ and $B = < 5, 4, - 9 >$ $B= <5 ,4 ,-9 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2017-06-03T13:49:31

The result is $= - 183.9$ $=-183.9$

The dot product is

$\to A . \to B = < 8, - 2.9 > . < 5, 4, - 9 > = (8 \cdot 5) + (- 2 \cdot 4) + (9 \cdot - 9)$ $vecA.vecB=<8,-2.9>.<5,4,-9> =(8*5)+(-2*4)+(9*-9)$

$= 40 - 8 - 81 = - 49$ $=40-8-81=-49$

The modulus of $\to A$ $vecA$ is

$∣ ∣ ∣ ∣ ∣ ∣ \to A ∣ ∣ ∣ ∣ ∣ ∣ = | | < 8, - 2, 9 > | | = \sqrt{64 + 4 + 81} = \sqrt{149}$ $||vecA||=||<8,-2,9>||=sqrt(64+4+81)=sqrt149$

The modulus of $\to B$ $vecB$ is

$∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣ = | | < 5, 4, - 9 > | | = \sqrt{25 + 16 + 81} = \sqrt{122}$ $||vecB||=||<5,4,-9>||=sqrt(25+16+81)=sqrt122$

Therefore,

$\to A . \to B - ∣ ∣ ∣ ∣ ∣ ∣ \to A ∣ ∣ ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣$ $vecA.vecB-||vecA||+||vecB||$

$= - 49 - \sqrt{149 \cdot 122}$ $=-49-sqrt(149*122)$

$= - 183.8$ $=-183.8$

If A= <8 ,- 2 ,9>A=<8,−2,9>A= <8 ,- 2 ,9> and B= <5 ,4 ,-9 >B=<5,4,−9>B= <5 ,4 ,-9 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?