Question:
Given \(\vec{A}=2\hat{i}-2\hat{j}+8\hat{k}\) and \(\vec{B}=2\hat{i}-m\hat{j}+8\hat{k}\), if \(\vec{A}\) and \(\vec{B}\) have the same direction, the value of \(m\) is
Given \(\vec{A}=2\hat{i}-2\hat{j}+8\hat{k}\) and \(\vec{B}=2\hat{i}-m\hat{j}+8\hat{k}\), if \(\vec{A}\) and \(\vec{B}\) have the same direction, the value of \(m\) is
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Vectors with the same direction are positive multiples of each other, so their matching components must be in the same ratio.
Updated On: Nov 12, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Two vectors have the same direction only when one is a positive multiple of the other, so their components are in the same ratio.
Step 2: Calculation
Write \(\vec{B}=\lambda\vec{A}\). The \(\hat{i}\) components give \(2=2\lambda\), so \(\lambda=1\).
The \(\hat{j}\) components give \(-m=\lambda(-2)=-2\).
Step 3: Result
Hence \(m=2\). The \(\hat{k}\) components (8 and 8) already agree, which confirms \(\lambda=1\).
Final Answer:
The value of m is 2. \[ \boxed{\text{(B) }2} \]
Two vectors have the same direction only when one is a positive multiple of the other, so their components are in the same ratio.
Step 2: Calculation
Write \(\vec{B}=\lambda\vec{A}\). The \(\hat{i}\) components give \(2=2\lambda\), so \(\lambda=1\).
The \(\hat{j}\) components give \(-m=\lambda(-2)=-2\).
Step 3: Result
Hence \(m=2\). The \(\hat{k}\) components (8 and 8) already agree, which confirms \(\lambda=1\).
Final Answer:
The value of m is 2. \[ \boxed{\text{(B) }2} \]
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