Maximum and minimum magnitude of resultant of two given vectors are 17 units and 7 unit respectively

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3-1.Vectors

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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

A

$14$

B

$16$

C

$18$

D

$13$

Solution

(d) ${R_{\max }} = A + B = 17$ 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$

Standard 11

Physics

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