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(D) Let the magnitudes of the two vectors be $A$ and $B$.The maximum magnitude of the resultant is given by $R_{\max} = A + B = 17$.The minimum magnit

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$13$

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(D) Let the magnitudes of the two vectors be $A$ and $B$.The maximum magnitude of the resultant is given by $R_{\max} = A + B = 17$.The minimum magnitude of the resultant is given by $R_{\min} = |A - B| = 7$.Adding these two equations: $(A + B) + (A - B) = 17 + 7 \implies 2A = 24 \implies A = 12$.Substituting $A = 12$ into the first equation: $12 + B = 17 \implies B = 5$.When the two vectors are at right angles to each other $(	heta = 90^\circ)$,the magnitude of their resultant $R$ is given by $R = \sqrt{A^2 + B^2}$.Substituting the values: $R = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$ units.

Column-$I$	Column-$II$
$(1)$ Resultant of two mutually perpendicular vectors	$(a)$ Along the bisector of the angle between them
$(2)$ Direction of $\overrightarrow A \times \overrightarrow B$	$(b)$ Coplanar
	$(c)$ Perpendicular to the plane containing $\overrightarrow A$ and $\overrightarrow B$

Column $I$	Column $II$
$(A) \|A+B\|$	$(p) \frac{\sqrt{3}}{2} x^2$
$(B) \|A-B\|$	$(q) x$
$(C) A \cdot B$	$(r) \sqrt{3} x$
$(D) \|A \times B\|$	$(s) \frac{x^2}{2}$

The maximum and minimum magnitude of the resultant of two given vectors are $17$ units and $7$ units respectively. If these two vectors are at right angles to each other,the magnitude of their resultant is

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