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:
- Vector component of $\overrightarrow{\mathbf{a}}$ along and perpendicular to $\overrightarrow{\mathbf{b}}$ are
$$ \left(\frac{\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}}{|\overrightarrow{\mathbf{b}}|^{2}}\right) \overrightarrow{\mathbf{b}} \quad \text { and } \quad \overrightarrow{\mathbf{a}}-\left(\frac{\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}}{|\overrightarrow{\mathbf{b}}|^{2}}\right) \overrightarrow{\mathbf{b}} $$
