Vector Dot Product (3D)

Algebra Level 1

For

$A=(1, 4, 7), B=(2, 6, 4), C=(1, 9, 8) ,$

what is the dot product of $A$ and $(B-C)?$

1 solution

Shubhrajit Sadhukhan
May 4, 2021

$\vec A = \hat i + 4 \hat j + 7 \hat k$

$\vec B = 2 \hat i + 6 \hat j + 4 \hat k$

$\vec C = \hat i + 9 \hat j + 8 \hat k$

$\vec B - \vec C = \hat i - 3 \hat j - 4 \hat k$

$\therefore \vec A \cdot (\vec B - \vec C) = 1 - 12 - 28 = - 39$

(Note that all terms with ij, ik, and jk in the dot product are zero)