Question

Let \vec{u} ​u ​⃗ ​​ = (1,2,-4) and \vec{v} ​v ​⃗ ​​ = (2,3,5). What is \vec{u} \cdot \vec{v} ​u ​⃗ ​​ ⋅ ​v ​⃗ ​​ ?

Answer 1

The value of $u\cdot v=-8$

Step-by-step explanation:

$\vec{u}=(1,2,-4)=i+2j-4k$

$\vec{v}=(2,3,5)=2i+3j+5k$

$u\cdot v=(i+2j-4k)\cdot (2i+3j+5k)$

We know that

$i\cdot i=j\cdot j=k\cdot k=1, i\cdot j=j\cdot k=k\cdot i=i\cdot k=k\cdot j=j\cdot i=0$

$u\cdot v=i\cdot 2i+i\cdot 3j+i\cdot 5k+2j\cdot 2i+2j\cdot 3j+2j\cdot 5k-4k\cdot 2i-4k\cdot 3j-4k\cdot 5k$

$u\cdot v=2+6-20$

$u\cdot v=12-20$

$u\cdot v=-8$

Hence, the value of $u\cdot v=-8$

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