SATHEE: Motion in a Plane - Result Question 22

Motion in a Plane - Result Question 22

24. The magnitudes of vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are 3,4 and 5 units respectively. If $\vec{A} + \vec{B} = \vec{C}$ , then the angle between $\vec{A}$ and $\vec{B}$ is

[1988]

(a) $π / 2$

(b) $\cos^{- 1} 0.6$

(d) $π / 4$

Topic 2: Motion in a Plane with Constant acceleration

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Answer:

Correct Answer: 24. (a)

Solution:

$\begin{aligned} (a) & (\vec{A} + \vec{B})^{2} = (\vec{C})^{2} \\ \Rightarrow & A^{2} + B^{2} + 2 \vec{A} \cdot \vec{B} = C^{2} \\ \Rightarrow & 3^{2} + 4^{2} + 2 \vec{A} \cdot \vec{B} = 5^{2} \\ \Rightarrow & 2 \vec{A} \cdot \vec{B} = 0 or \Rightarrow \vec{A} \cdot \vec{B} = 0 ∴ \vec{A} ⊥ \vec{B} \end{aligned}$

Here $A^{2} + B^{2} = C^{2}$ . Hence, $\vec{A} ⊥ \vec{B}$

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Motion in a Plane - Result Question 22

24. The magnitudes of vectors A→,B→ and C→ are 3,4 and 5 units respectively. If A→+B→=C→, then the angle between A→ and B→ is

Answer:

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24. The magnitudes of vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are 3,4 and 5 units respectively. If $\vec{A} + \vec{B} = \vec{C}$ , then the angle between $\vec{A}$ and $\vec{B}$ is