Question

Find the angle between the vectors < 1, 2, –2 > and < 4 ,0, –3 >.

Answer #1

Find the angle θ between the vectors (,) and (-2,-4).

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>

A) Find the angle between the vectors 8i-j + 4k and 4j + 2k
B) Find c so that the vectors 2i-3j + ck and 2i-j + 4k are perpendicular
C) Find the scalar projection and the vector projection of 2i +
4j-4 on 3i-3j + k

(a) Find the volume of the parallelepiped determined by the
vectors a =< 2, −1, 3 >, b =< −3, 0, 1 >, c =< 2, 4,
1 >.
(b) Find an equation of the plane that passes through the point
(2, 4, −3) and is perpendicular to the planes 3x + 2y − z = 1 and x
− 2y + 3z = 4.

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.

Determine if the vectors v1= (3, 0, -3, 6),
v2 = ( 0, 2, 3, 1), and v3 = (0, -2, 2, 0 )
form a linearly dependent set in R 4. Is it a basis of
R4 ?

(a) Do the vectors v1 = 1 2 3 , v2 = √ 3 √ 3 √ 3 , v3=√ 3 √ 5 √
7, v4 = 1 0 0 form a basis for R 3 ? Why or why not?
(b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and
a2, where a1 = (1 0 −1 0) , a2 = 0 1 0 −1. Find a basis for the
orthogonal complement V ⊥...

Do the vectors v1 = 1 2 3 ,
v2 = √ 3 √ 3 √ 3 ,
v3 √ 3 √ 5 √ 7 ,
v4 = 1 0 0 form a basis for R 3 ? Why or why not?
(b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and
a2, where a1 = ...

If X and Y are vectors of magnitude 1 and 2,
respectively, with an angle of 120º between them. Determine I3X +
2YI and the direction of vector 3X + 2Y.
Vectors are 2D

Let the vectors a and b be: a = <0,-3,4> and
b=<1,2,-2>. Find the following:
a) The vector c=2a+b and its length.
b) The cosine of the angle between the vector c and the y
axis
c) One unit vector that is orthogonal to both a and b.

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