If A= <-5 ,-4 ,-1 > and B= <2 ,-9 ,8 >, what is A*B -||A|| ||B||?

Oct 13, 2016

$\overline{A} \cdot \overline{B} - | \overline{A} | | \overline{B} | \approx - 61.1$

Explanation:

For the dot-product of two vectors, one multiplies the corresponding components:

$\overline{A} \cdot \overline{B} = \left(- 5\right) \left(2\right) + \left(- 4\right) \left(- 9\right) + \left(- 1\right) \left(8\right)$

$\overline{A} \cdot \overline{B} = 18$

The magnitude of a vector is the square root of the sum of the squares of the components:

$| \overline{A} | = \sqrt{{\left(- 5\right)}^{2} + {\left(- 4\right)}^{2} + {\left(- 1\right)}^{2}}$

$| \overline{A} | = \sqrt{42}$

|barB| = sqrt((2^2 + (-9)^2 + (8)^2)

$| \overline{B} | = \sqrt{149}$

$\overline{A} \cdot \overline{B} - | \overline{A} | | \overline{B} | = 18 - \sqrt{42} \sqrt{149}$

$\overline{A} \cdot \overline{B} - | \overline{A} | | \overline{B} | \approx - 61.1$