Question

HELP!!

1. Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <6, 4>, v = <-9, 8>

2. . Find the first six terms of the sequence.
a1 = -2, an = 3 • an-1

THANK YOU!

Answer 1

I think it is neither

Answer 2

Question 1. Option A.

Question 2. Option B.

Explanation:

Question 1.

In this questions given vectors are u = <6, 4> and v = <-9, 8>

To check if the given vectors are orthogonal we will find the resultant of u.v

if the product of two vectors = 0 then vectors are orthogonal.

u.v = (6).(-9) + (4).(8) = -54 + 32 = -22 ≠ 0

Therefore vectors are not orthogonal.

Now we see that coordinates of vectors are not same showing they are not parallel. So vectors are neither parallel nor orthogonal.

NEITHER is the answer for question 1.

Question 2.

Explicit formula of the sequence is
`a_(n)=3.a_(n-1)`

and the first term is a1 = -2

Now second term of the sequence =
`a_(2)= 3.a_(2-1)=3.a_(1)=3.(-2)=(-6)`

Third term =
`3.a_(3-1)=3.a_(2)=3.(-6)=(-18)`

Fourth term =
`a_(4)=3.a_(4-1)=3.a_(3)=3.(-18)=(-54)`

Fifth term =
`a_(5)=3.a_(5-1)=3.a_(4)=3.(-54)=(-162)`

Sixth term =
`a_(6)=3.a_(6-1)=3.a_(5)=3.(-162)=(-486)`

So the sequence is Option B. -2, -6, -18, -54, -162, -486