Clearer pics Edit Window Help Two vectors Componene ori al

Edit Window Help Two vectors Componene ori along direction of a is Multiplying these gives the dot product. Component of a ong direction of or multiplying these gives the dot product. (a axS (Express your answer in veetor form. (d) the component ara along the direction of b 3.6 ab pand the toure below.)

Solution

a = 2.5i + 3.5 j

b = 6i + 5.5 j

a)

So,

a (cross) b

= (2.5i + 3.5j) (cross) (6i + 5.5 j)

= 2.5*5.5 k + 3.5*6*(-k)

= (2.5*5.5 - 3.5*6) k

= -7.25 k

b)

a.b

=  (2.5i + 3.5j) . (6i + 5.5 j)

= 2.5*6 + 3.5*5.5

= 34.25

c)

(a+b).b

= a.b + b.b

= a.b + b^2

= 34.25 + (6^2+5.5^2)

= 100.5

d)

component of a along b

= (a.b)/(|b|)

= 34.25/(sqrt(6^2 +5.5^2))

= 4.21