Question

10 a 12 m vector and a 5 m vector are combined. which of the following is not a possible combination of the two using vector addition. a 13 m b 7 m c 60 m d 17 m

Explanation:

Step1: Recall vector - addition magnitude rule

The magnitude of the sum of two vectors $\vec{A}$ and $\vec{B}$, $|\vec{R}|=|\vec{A}+\vec{B}|$ satisfies the inequality $|\ |\vec{A}|-|\vec{B}|\ |\leq|\vec{A}+\vec{B}|\leq|\vec{A}| + |\vec{B}|$.

Step2: Identify the magnitudes of the given vectors

Let $|\vec{A}| = 12$ m and $|\vec{B}|=5$ m. Then $|\ |\vec{A}|-|\vec{B}|\ |=|12 - 5|=7$ m and $|\vec{A}|+|\vec{B}|=12 + 5=17$ m.

Step3: Analyze the possible range

The magnitude of the resultant vector of the two - vector addition lies in the range $7$ m $\leq|\vec{R}|\leq17$ m.

Answer:

C. 60 m