Question

Find two vectors v1 and v2 whose sum is 〈1,3〉, where v1 is parallel to 〈1,2〉 while v2 is perpendicular to 〈1,2〉.

v1 =

and

v2 =

Answer #1

Find two vectors v¯1 and v¯2 whose sum is 〈2,3〉, where v¯1 is
parallel to 〈−1,3〉 while v¯2 is perpendicular to 〈−1,3〉.
v¯1 = and
v¯2 =

1) Find the angle θ between the vectors a=9i−j−4k and
b=2i+j−4k.
2) Find two vectors v1 and v2 whose sum is <-5,
2> where v1 is parallel to <-3 ,0> while v2 is
perpendicular to < -3,0>

Find two non-parallel vectors v1 and v2 in R2 such that
||v1||2=||v2||2=1 and whose angle with [3,4] is 42 degrees. *Note:
[3,4] is a 2 by 1 matrix with 3 on the top and 4 on the bottom.

Find two vectors v¯¯¯1 and v¯¯¯2 whose sum is 〈5,1〉, where v¯¯¯1
is parallel to 〈5,−1〉 while v¯¯¯2 is perpendicular to 〈5,−1〉 .
v¯¯¯1 = and v¯¯¯2 =

2. Two vectors, ~v1 and ~v2. ~v1 has a length of 12 and is
oriented at an angle θ1 = 30o relative to the positive x−axis. ~v2
has a length of 6 and is oriented at an angle θ2 = 0o relative to
the positive x−axis (it is aligned with the positive x−axis)
a. What are the magnitude and direction (angle) of the sum of
the two vectors ( 1+2 ~v = ~v1 + ~v2)?
b. What are the magnitude...

If S is the set of vectors in R^4 (S= {v1, v2, v3, v4, v5})
where, v1 = (1,2,-1,1), v2 = (-3,0,-4,3), v3 = (2,1,1,-1), v4 =
(-3,3,-9,-6), v5 = (3,9,7,-6)
Find a subset of S that is a basis for the span(S).

2. Vector Practice
a. Determine the magnitude and direction of the sum (V1+V2)of
the two vectors V1=3i+2j and V2=4i+j
b. Determine the components of a vector, with a magnitude of
10.0 and a direction of 40.0 degrees above the positive x-axis.

consider the basis S={v1,v2} for R^2,where v1=(-2,1) and
v2=(1,3),and let T:R^2-R^3 be linear transformation such that
T(v1)=(-1,2,0) And T(v2)=(0,-3,5), find T(2,-3)

let v1=[1,0,10], v2=[0,1,0,1] and let W be the
subspace of R^4 spanned by v1 and v2.
A. convert {v1,v2} into an orhonormal basis of W.
Basis =
B.find the projection of b=[-1,-2,-2,-1] onto W
C.find two linear independent vectors in R^4
perpendicular to W.
vectors =

266) (H) Find the resultant of the two vectors. (M1=8.57;
A1=58.7) = V1; (M2=3.94; A2=52.1) = V2; (M3,A3)=V3=V1+V2
M=magnitude and A=angle in degrees. answers=M3 and A3 (deg) The
resultant of two vectors is the same a the sum of them. There are 2
answers.

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