Question

If \(\vec{A}=5\hat{i}+2\hat{j}\) and \(\vec{B}=a\hat{i}+3\hat{j}\) are perpendicular to each other, the value of 'a' is

• A. \(\frac{-6}{5}\)
• B. \(\frac{6}{5}\)
• C. \(\frac{4}{5}\)
• D. \(\frac{-4}{5}\)

Hint:

Two vectors are perpendicular when their dot product is zero. Equate the dot product to zero and solve for a.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Two vectors are perpendicular when their scalar (dot) product is zero.
\(\vec{A}\cdot\vec{B}=0\)

Step 2: Calculation
\(\vec{A}\cdot\vec{B}=(5)(a)+(2)(3)=5a+6\)
Setting this to zero: \(5a+6=0\)

Step 3: Solve for a
\(5a=-6\)
\(a=-\dfrac{6}{5}\)

Final Answer:
The value of a is minus six by five. \[ \boxed{\text{(A) }\dfrac{-6}{5}} \]