Question

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 1

Correct Answer - Option 3 : -6

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 1.