Question

Determine the total magnitude of the vector 6i + 8j.

Assuming the horizontal plane to be XY plane.

1. 28
2. 5
3. 10
4. 8

Answer 1

Correct Answer - Option 3 : 10

Concept:

If \(\vec{a}=~{{a}_{1}}\hat{i}+{{a}_{2}}\hat{j}+{{a}_{3}}\hat{k}\) is a vector then the magnitude of the vector is given by \(\left| {\vec{a}} \right|=\sqrt{a_{1}^{2}+a_{2}^{2}+a_{3}^{2}}~\)

Calculation:

Given:

As we know that, if \(\vec{a}=~{{a}_{1}}\hat{i}+{{a}_{2}}\hat{j}+{{a}_{3}}\hat{k}\) is a vector then the magnitude of the vector is given by \(\left| {\vec{a}} \right|=\sqrt{a_{1}^{2}+a_{2}^{2}+a_{3}^{2}}\)

a₁ = 6, a₂ = 8

\(\left| {\vec{a}} \right|=\sqrt{a_{1}^{2}+a_{2}^{2}}\)

\(\left| {\vec{a}} \right|=\sqrt{6^{2}+8^{2}}\)

\(\left| {\vec{a}} \right|=\sqrt{36+64}\)

\(\left| {\vec{a}} \right|=10\)