If $A = < 8, - 5, 6 >$ $A= <8 ,-5 ,6 >$ and $B = < 7, 1, 3 >$ $B= <7 ,1 ,3 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2017-03-04T07:23:26

The answer is $= 16.8$ $=16.8$

The dot product is

$\to A . \to B = < 8, - 5, 6 > . < 7, 1, 3 \geq 56 - 5 + 18 = 69$ $vecA.vecB= <8,-5,6>.<7,1,3>=56-5+18=69$

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

$∣ ∣ ∣ ∣ ∣ ∣ \to A ∣ ∣ ∣ ∣ ∣ ∣ = | | < 8, - 5, 6 | | = \sqrt{64 + 25 + 36} = \sqrt{125}$ $||vecA||=||<8,-5,6||=sqrt(64+25+36)=sqrt125$

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

$∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣ = | | < 7, 1, 3 | | = \sqrt{49 + 1 + 9} = \sqrt{59}$ $||vecB||=||<7,1,3||=sqrt(49+1+9)=sqrt59$

Therefore,

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

$= 69 - \sqrt{125} \sqrt{59}$ $=69-sqrt125sqrt59$

$= - 16.8$ $=-16.8$

If A=<8,−5,6>A= <8 ,-5 ,6 > and B=<7,1,3>B= <7 ,1 ,3 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?