The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is
The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is
$14$
$16$
$18$
$13$
The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is
${R_{\max }} = A + B = 17$ when $\theta = 0^\circ $
${R_{\min }} = A - B = 7$ when $\theta = 180^\circ $
by solving we get $A = 12$ and $B = 5$
Now when $\theta = 90^\circ $ then $R = \sqrt {{A^2} + {B^2}} $
$⇒$ $R = \sqrt {{{(12)}^2} + {{(5)}^2}} $$ = \sqrt {169} $$ = 13$
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