Find the value of a if vector \(\overrightarrow{A}=2\widehat{i}+\widehat{j}-3\widehat{k}\) and vector \(\overrightarrow{B}=a\widehat{i}-3\widehat{j}+9\widehat{k}\) are parallel vectors.

  1. 6
  2. 9
  3. -6
  4. 2

Answer (Detailed Solution Below)

Option 3 : -6
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Detailed Solution

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CONCEPT:

  • Condition for parallel vectors: If two given vectors \(\overrightarrow{A}=a\widehat{i}+b\widehat{j}+c\widehat{k}\) and \(\overrightarrow{B}=x\widehat{i}+y\widehat{j}+z\widehat{k}\) are parallel vectors then:

\( {a \over x}= {b \over y}= {c \over z}\)

CALCULATION:

Given that two vectors are \(\overrightarrow{A}=2\widehat{i}+\widehat{j}-3\widehat{k}\) and \(\overrightarrow{B}=a\widehat{i}-3\widehat{j}+9\widehat{k}\)

If these two vectors are parallel to each other then from the given condition:

\( {2 \over a}= {1 \over -3}= {-3 \over 9}\)

a = - 6

  • So the correct answer is option 3.
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