Question:
If \(|\bar{a}|=24\), \(|\bar{b}|=7\), \(\bar{a}\cdot \bar{b}=0\), \(\bar{a}+\bar{b}+\bar{c}=\bar{0}\), then \(|\bar{c}|=\ldots\)
If \(|\bar{a}|=24\), \(|\bar{b}|=7\), \(\bar{a}\cdot \bar{b}=0\), \(\bar{a}+\bar{b}+\bar{c}=\bar{0}\), then \(|\bar{c}|=\ldots\)
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Write c = -(a + b), then square it using a . b = 0.
Updated On: Nov 12, 2026
- \(31\)
- \(17\)
- \(40\)
- \(25\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
From \(\bar{a}+\bar{b}+\bar{c}=\bar{0}\), \(\bar{c}=-(\bar{a}+\bar{b})\).
Step 2: Square the magnitude
\(|\bar{c}|^{2}=|\bar{a}|^{2}+|\bar{b}|^{2}+2\bar{a}\cdot \bar{b}\).
Step 3: Substitute
\(|\bar{c}|^{2}=576+49+0=625\).
Step 4: Take the root
\(|\bar{c}|=25\).
Final Answer:
The magnitude of \(\bar{c}\) is 25. \[ \boxed{\text{(D) }25} \]
From \(\bar{a}+\bar{b}+\bar{c}=\bar{0}\), \(\bar{c}=-(\bar{a}+\bar{b})\).
Step 2: Square the magnitude
\(|\bar{c}|^{2}=|\bar{a}|^{2}+|\bar{b}|^{2}+2\bar{a}\cdot \bar{b}\).
Step 3: Substitute
\(|\bar{c}|^{2}=576+49+0=625\).
Step 4: Take the root
\(|\bar{c}|=25\).
Final Answer:
The magnitude of \(\bar{c}\) is 25. \[ \boxed{\text{(D) }25} \]
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