Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Let → a = 4 → I + 3 → J and → B = 3 → I + 4 → J . (A) Find the Magnitudes of (A) → a , (B) → B ,(C) → a + → B and (D) → a − → B . - Physics

Let $\vec{a} = 4 \vec{i} + 3 \vec{j} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j}$. Find the magnitudes of (a)  $\vec{a}$ ,  (b)  $\vec{b}$ ,(c) $\vec{a} + \vec{b} \text { and }$ (d) $\vec{a} - \vec{b}$.

#### Solution

Given: $\vec{a} = 4 \vec{i} + 3 \vec{j} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j}$

(a) Magnitude of  $\vec{a}$ is given by $\left| \vec{a} \right| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = 5$

Magnitude of  $\vec{b}$ is  given by $\left| \vec{b} \right| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$

(c) $\vec{a} + \vec{b} = (4 \hat {i} + 3 \hat {j} ) + (3 \hat { i} + 4 \hat { j} ) = (7 \hat { i} + 7 \hat {j} )$

∴ Magnitude of vector $\vec{a} + \vec{b}$ is given by $\left| \vec{a} + \vec{b} \right| = \sqrt{49 + 49} = \sqrt{98} = 7\sqrt{2}$

(d) $\vec{a} - \vec{b} = \left( 4 \vec{i} + 3 \vec{j} \right) - \left( 3 \vec{i} + 4 \vec{j} \right) = \vec{i} - \vec{j}$

∴ Magnitude of vector $\vec{a} - \vec{b}$  is given by $\left| \vec{a} - \vec{b} \right| = \sqrt{\left( 1 \right)^2 + \left( - 1 \right)^2} = \sqrt{2}$

Concept: What is Physics?
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Chapter 2: Physics and Mathematics - Exercise [Page 29]

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 4 | Page 29
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