If \( a = 4 j \) and \( b = 3 j + 4 k \) , then the vector form of the component of \( a \) along \( b \) is

The vector component of \( a \) along \( b \) is \(( a · b | b | 2 ) b \). \( a · b = 4 × 3 = 12\) and \(| b | 2 = 9 + 16 = 25\). Component = \(12/25(3 j + 4 k )\) Answer: (B)

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Question 50

Mathematics Scalar and Vector Products Hard

If \(\vec{a} = 4\hat{j}\) and \(\vec{b} = 3\hat{j} + 4\hat{k}\), then the vector form of the component of \(\vec{a}\) along \(\vec{b}\) is

(A) \(\dfrac{12}{10\sqrt{3}}(3\hat{j}+4\hat{k})\)

(B) \(\rm \dfrac {12}{25}(3\vec j + 4 \vec k)\)

(C) \(\dfrac{12}{\sqrt{13}}(3\hat{j}+4\hat{k})\)

(D) \((3\hat{j}+4\hat{k})\)

✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The vector component of \(\vec{a}\) along \(\vec{b}\) is \(\left(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2}\right)\vec{b}\).

\(\vec{a} \cdot \vec{b} = 4 \times 3 = 12\) and \(|\vec{b}|^2 = 9 + 16 = 25\).

Component = \(\frac{12}{25}(3\hat{j} + 4\hat{k})\)

Answer: (B)

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Question 50

📘 Step-by-Step Solution & Detailed Explanation:

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