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Two vectors have magnitudes of 25 and 12. Which of the following is the only possible resultant for these vectors? A.25 B.12 C.42 D.28

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Answer:

Step 1: Draw the vectors[Ref. Fig.]

Consider there are two vectors A and B such that B is perpendicular to the resultant R

Since the resultant is perpendicular to vector B we will get a right-angled triangle

Step 2: Equation formation

From the triangle

                ∣A∣2=∣B∣2+∣R∣2                                             ....(1)

Given ,    ∣R∣=∣A+B∣=12                                            ....(2)   

                ∣A∣+∣B∣=18                                                     ....(3)  

Step 3: Solving Equations

Equation (3) and (1)⇒     ∣A∣2=(18−∣A∣)2+(12)2

                                    ⇒  ∣A∣2=182+∣A∣2−2×18∣A∣+

Explanation:

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