Quiz#2.

Q1.      Vector A has negative x componet 5.0 units in length and a positive y component 8.0 units in length.

(a) Write down an expression for A  in unit vector notation.

A = - 5 i + 8 j

(b) Determine the magnitude and direction of vector A.

A =  Ö  (Ax2 +Ay2 ) =    Ö (-5)2+82   = 9.43

tan a   = ïAy/Axï= 8/5;  a = 58o   ; \  q  = 122o

(c) What vector B when added to A gives a resultant vector with no x                     component and a negative y component 4.00 units in length? (Give B in unit vector notation)

Given                          B + A  = - 4 j,

then                              B = - 4 jA = - 4 j – ( - 5 i + 8 j )

Hence,             B = 5 i  - 12 j

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Q2.      Given two vectors P = 4.0 i + 5 j and Q = 6.0 i - 8.0 j,

(i)                  find A · B, and

P · Q = (4.0 i + 5 j ) · (6.0 i - 8.0 j )

= (4x6)(i·i) + (4x(-8))(i·j) + (5x6)(j·i) +(5x(-8))(j·j)

= 24 + 0 + 0 - 40

= - 16

(ii)            find the angle between the two vectors.

P · Q = P Q cos q

\ cos q  = P · Q / ( A B )

=  -16 / (Ö 42+52 ) (Ö 62+82   )  = - 0.250

q  = 105o.