# If $$\vec{a}$$=$$\hat{i}$$+4$$\hat{j}$$ and $$\vec{b}$$=3$$\hat{i}$$-3$$\hat{j}$$. Find the magnitude of $$\vec{a}+\vec{b}$$.

Category: QuestionsIf $$\vec{a}$$=$$\hat{i}$$+4$$\hat{j}$$ and $$\vec{b}$$=3$$\hat{i}$$-3$$\hat{j}$$. Find the magnitude of $$\vec{a}+\vec{b}$$.
Editor">Editor Staff asked 11 months ago

If $$\vec{a}$$=$$\hat{i}$$+4$$\hat{j}$$ and $$\vec{b}$$=3$$\hat{i}$$-3$$\hat{j}$$. Find the magnitude of $$\vec{a}+\vec{b}$$.

(a) $$\sqrt{6}$$

(b) $$\sqrt{11}$$

(c) $$\sqrt{5}$$

(d) $$\sqrt{17}$$

My question is from Addition of Vectors topic in portion Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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The correct choice is (d) $$\sqrt{17}$$
Explanation: Given that, $$\vec{a}$$=$$\hat{i}$$+4$$\hat{j}$$ and $$\vec{b}$$=3$$\hat{i}$$-3$$\hat{j}$$
∴$$\vec{a}+\vec{b}$$=(1+3) $$\hat{i}$$+(4-3) $$\hat{j}$$
=4$$\hat{i}$$+$$\hat{j}$$
|$$\vec{a}+\vec{b}$$|=$$\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}$$