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

Question

1498 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-18T09:23:17

The answer is $= - 81.4$ $=-81.4$

The vectors are

$\to A = < 2, - 3, - 3 >$ $vecA=<2,-3,-3>$

$\to B = < - 2, 5, 7 >$ $vecB=<-2,5,7>$

The dot product is

$\to A . \to B = < 2, - 3, - 3 > . < - 2, 5, 7 \geq - 4 - 15 - 21 = - 40$ $vecA.vecB=<2,-3,-3>.<-2,5,7>=-4-15-21=-40$

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

$= | | < 2, - 3, - 3 > | | = \sqrt{4 + 9 + 9} = \sqrt{22}$ $=||<2,-3,-3>||=sqrt(4+9+9)=sqrt22$

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

$= | | < - 2, 5, 7 > | | = \sqrt{4 + 25 + 49} = \sqrt{78}$ $=||<-2,5,7>||=sqrt(4+25+49)=sqrt78$

Therefore,

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

$= - 40 - \sqrt{22} \cdot \sqrt{78}$ $=-40-sqrt22*sqrt78$

$= - 81.4$ $=-81.4$

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