Find the dot product of $a = 3 i - 4 j + 2 k$ and $b = - i + 7 j - 5 k$ .

medium 2 marks Class 12 · Mathematics · Vector Algebra

Answer

- 41

The correct answer is $- 41$ — Thus the dot product $a \cdot b$ is $- 41$ .

Step-by-step solution

Multiply corresponding components: $3 \times (- 1) = - 3$ , $(- 4) \times 7 = - 28$ , $2 \times (- 5) = - 10$ .
Sum the products: $- 3 + (- 28) + (- 10) = - 41$ .
Thus the dot product $a \cdot b$ is $- 41$ .

Common mistake: Incorrectly handling the signs of the components

Concept tested: Dot product of two vectors