A force of F-3 - - 4 - is acting on a box at pointA- whose position vector with respect to origin is - Work done in displacing the particle fromA- to B- whose position vector with respect to origin is will be - units

The box has to be displaced from A⃗ to B⃗. So the vector A⃗B⃗ will be the displacement vector of the box. O⃗A⃗= [ 2; 3 ] O⃗B⃗=[ 5; 6 ], wher ...

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Byju's Answer

Standard XIII

Mathematics

Dot Product of Two Vectors

A force of F⃗...

Question

$A f o r c e o f \to F = 3^i + 4^j i s a c t i n g o n a b o x a t p o i n t \to A w h o s e p o s i t i o n v e c t o r w i t h r e s p e c t t o o r i g i n i s < 2, 3 > . W o r k d o n e i n d i s p l a c i n g t h e p a r t i c l e f r o m \to A t o \to B w h o s e p o s i t i o n v e c t o r w i t h r e s p e c t t o o r i g i n i s < 5, 6 > w i l l b e . . . . . . . u n i t s$

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Solution

$T h e b o x h a s t o b e d i s p l a c e d f r o m \to A t o \to B . S o t h e v e c t o r \to A B w i l l b e t h e d i s p l a c e m e n t v e c t o r o f t h e b o x . \to O A = [\begin{matrix} 23 \end{matrix}] \to O B = [\begin{matrix} 56 \end{matrix}], w h e r e O i s t h e o r i g i n \to A B = \to O B - \to O A = [\begin{matrix} 56 \end{matrix}] - [\begin{matrix} 23 \end{matrix}] = [\begin{matrix} 33 \end{matrix}] = 3 i + 3 j . N o w t h e w o r k d o n e w i l l \to F . \to A B = (3^i + 4^j) . (3^i + 3^j) = 9 + 0 + 0 + 12 = 21 u n i t s$

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$A f o r c e o f \to F = 3^i + 4^j i s a c t i n g o n a b o x a t p o i n t \to A w h o s e p o s i t i o n v e c t o r w i t h r e s p e c t t o o r i g i n i s < 2, 3 > . W o r k d o n e i n d i s p l a c i n g t h e p a r t i c l e f r o m \to A t o \to B w h o s e p o s i t i o n v e c t o r w i t h r e s p e c t t o o r i g i n i s < 5, 6 > w i l l b e . . . . . . . u n i t s$