Question

Find a • b. a = 5i + 7j, b = -4i + 3j

Answer 1

`\boxed{-20i^2 -13ij+21j^2}`

Explanation:

`\sf Plug \ in \ the \ values.`

`(5i+7j) \cdot (-4i+3j)`

`\sf Expand \ brackets.`

`5i(-4i+3j)+7j(-4i+3j)`

`-20i^2 +15ij+-28ij +21j^2`

`\sf Combine \ like \ terms.`

`-20i^2 -13ij+21j^2`

Answer 2

`a \cdot b = 1`

Explanation:

`a = 5i + 7j`

`b = -4i + 3j`

`a = a_xi + a_yj`

`b = b_xi + b_yj`

`a \cdot b = a_xb_x + a_yb_y`

`a \cdot b = (5)(-4) + (7)(3)`

`a \cdot b = -20 + 21`

`a \cdot b = 1`