Vectors 1 Question 20

21. The components of a vector $\overrightarrow{\mathbf{a}}$ along and perpendicular to a non-zero vector $\overrightarrow{\mathbf{b}}$ are …….and…….respectively.

(1988, 2M)

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Answer:

Correct Answer: 21. (c)

Solution:

  1. Vector component of $\overrightarrow{\mathbf{a}}$ along and perpendicular to $\overrightarrow{\mathbf{b}}$ are

$$ \left(\frac{\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}}{|\overrightarrow{\mathbf{b}}|^{2}}\right) \overrightarrow{\mathbf{b}} \quad \text { and } \quad \overrightarrow{\mathbf{a}}-\left(\frac{\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}}{|\overrightarrow{\mathbf{b}}|^{2}}\right) \overrightarrow{\mathbf{b}} $$



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