If A → = 4 i ^ - 3 j ^ and B → = 6 i ^ + 8 j ^ then magnitude and direction of A → + B → will be

A → + B → = 4 i ^ - 3 j ^ + 6 i ^ + 8 j ^ = 10 i ^ + 5 j ^ A → + B → = 10 2 + 5 2 = 5 5 tan ⁡ θ = 5 10 = 1 2 ⇒ θ = tan - 1 ⁡ 1 2

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsAddition/SubtractionEasy2 minPYQ_2020

PhysicsEasysingle choice

If $\vec{A} = 4 \hat{i} - 3 \hat{j}$ and $\vec{B} = 6 \hat{i} + 8 \hat{j}$ then magnitude and direction of $\vec{A} + \vec{B}$ will be

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Answer:

Solution:

$\vec{A} + \vec{B} = (4 \hat{i} - 3 \hat{j}) + (6 \hat{i} + 8 \hat{j}) = 10 \hat{i} + 5 \hat{j}$

$|\vec{A} + \vec{B}| = \sqrt{{(10)}^{2} + {(5)}^{2}} = 5 \sqrt{5}$

$\tan θ = \frac{5}{10} = \frac{1}{2}$

$\Rightarrow$ $θ = \tan^{- 1} (\frac{1}{2})$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:VectorsSubtopic:Addition/Subtraction

⏱ 2mℹ️ Source: PYQ_2020

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