Find the scalar (dot) product of vectors $a = i + 2 j - 3 k$ and $b = 4 i - j + k$ .

easy MCQ 1 mark Class 12 · Mathematics · Vector Algebra

Answer

- 1

The correct answer is a) $- 1$ — Hence the scalar product is $- 1$ .

Step-by-step solution

Write the components of $a$ as $(1, 2, - 3)$ and of $b$ as $(4, - 1, 1)$ .
Use the dot product formula $a \cdot b = a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3}$ .
Calculate $1 \times 4 + 2 \times (- 1) + (- 3) \times 1 = 4 - 2 - 3 = - 1$ .
Hence the scalar product is $- 1$ .

Common mistake: Ignoring the negative sign of the third component while multiplying.

Concept tested: Scalar (dot) product