If \(\rm a=m \vec{i}+16 \vec{j} \) and |a| = 20, then find the value of m.

Question

Question

This question was previously asked in

AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper

Answer 1

Given:

\(\rm a=m \vec{i}+16 \vec{j} \) and |a| = 20,

Concept:

The modulus of any vector \(\vec a=x\hat i+y\hat j\) is given by

\(|a|=\sqrt{x^2+y^2}\)

Calculation:

\(\rm a=m \vec{i}+16 \vec{j} \) and |a| = 20,

Now,

\(\rm |a|=|m \vec{i}+16 \vec{j} |\)

\(\rm 20 = \sqrt{m^2+(16)^2}\)

⇒ \(\rm m^2=400-256=144\)

⇒ m = 12

Hence the option (4) is correct

Download Solution PDF