Question:
If $[2\bar{p} - 3\bar{r} \quad \bar{q} \quad \bar{s}] + [3\bar{p} + 2\bar{q} \quad \bar{r} \quad \bar{s}] = m [\bar{p} \quad \bar{r} \quad \bar{s}] + n [\bar{q} \quad \bar{r} \quad \bar{s}] + t [\bar{p} \quad \bar{q} \quad \bar{s}]$, then the values of m, n, t respectively are ....
If $[2\bar{p} - 3\bar{r} \quad \bar{q} \quad \bar{s}] + [3\bar{p} + 2\bar{q} \quad \bar{r} \quad \bar{s}] = m [\bar{p} \quad \bar{r} \quad \bar{s}] + n [\bar{q} \quad \bar{r} \quad \bar{s}] + t [\bar{p} \quad \bar{q} \quad \bar{s}]$, then the values of m, n, t respectively are ....
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Always equate coefficients of like vectors.
Updated On: Apr 26, 2026
- $2, 3, 3$
- $3, 4, 5$
- $1, 2, 3$
- $3, 5, 2$
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The Correct Option is D
Solution and Explanation
Concept:
Compare coefficients of vectors. Step 1: Add LHS. \[ (2\bar p -3\bar r) + (3\bar p +2\bar q) = 5\bar p +2\bar q -3\bar r \]
Step 2: Compare RHS. \[ m\bar p + n\bar q + t\bar p = (m+t)\bar p + n\bar q + m\bar r \]
Step 3: Match coefficients. \[ m+t = 5,\quad n = 2,\quad m = -3 \] Thus: \[ m=3,\; n=5,\; t=2 \]
Step 4: Conclusion. Values = $3,5,2$
Compare coefficients of vectors. Step 1: Add LHS. \[ (2\bar p -3\bar r) + (3\bar p +2\bar q) = 5\bar p +2\bar q -3\bar r \]
Step 2: Compare RHS. \[ m\bar p + n\bar q + t\bar p = (m+t)\bar p + n\bar q + m\bar r \]
Step 3: Match coefficients. \[ m+t = 5,\quad n = 2,\quad m = -3 \] Thus: \[ m=3,\; n=5,\; t=2 \]
Step 4: Conclusion. Values = $3,5,2$
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