Homework (HWAC1)

Solve without using MATLAB

IGivena=<2,-4,4>b= 2j - k

Find(1) 2a + 3b

(2) a - 2b

(3) IaI

(4) Ia - bI

IIFind the vector that has the same direction as<-4,2,4> but has the length 6.

III If v lies lies in the first quadrant and makes an angle of 30 with the positive x axis and the magnitude of v is 4,write v in component form.

IVFind a vector a with representation given by the directed line segment connecting the points

A(0,3,1) and B(2,3,-1)

V Find abif

(1)a= 2i +jb=I - j + k

(2)a=<4,1,1/4>b=<6,-3,-8>

(3)a=ib=jwhere i and j are unit vectors

For number 2find also the scalar and vector projections of a on b

VI Find the direction angles ,, for the vector3i + 2j - k

VII Determine if the given vectors are orthogonal, parallel or neither

(1)a=<-5,3,7>,b = <6,-8,2>

(2)a=<4,6>, b=<-3,2>

(3)a= -i + 2j +5k, b= 3i +4j

VIIIFind a unit vector that is perpendicular to the vectorsa=<4,1,1/4>b=<6,-3,-8>