Question
Download Solution PDFFind 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- 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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