JAMIA 2024 — Mathematics PYQ

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Question

JAMIA 2024 — Mathematics PYQ

JAMIA | Mathematics | 2024

The scalar product of 5i + j – 3k and 3i – 4j + 7k is:

Choose the correct answer:

Explanation

Given Vectors

Let the vectors be:

\vec{a} = 5\hat{i} + \hat{j} - 3\hat{k}

\vec{b} = 3\hat{i} - 4\hat{j} + 7\hat{k}

Step 1: Scalar Product Formula

The scalar product $\vec{a} \cdot \vec{b}$ is calculated as:

\vec{a} \cdot \vec{b} = (a_x \times b_x) + (a_y \times b_y) + (a_z \times b_z)

Step 2: Calculation

Substitute the components from the vectors:

\vec{a} \cdot \vec{b} = (5 \times 3) + (1 \times -4) + (-3 \times 7)

\vec{a} \cdot \vec{b} = 15 - 4 - 21

\vec{a} \cdot \vec{b} = 11 - 21

\vec{a} \cdot \vec{b} = -10

Final Answer

The scalar product is:

-10

Choose the correct answer:

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