Question

Find the unit vector parallel to the vector to a vector minus to b vector + 300 vector where a vector equal to i + j + k b vector equal to 2a - 2 + 3 k and c vector equal to i - 2 + k

Answer 1

Answer:

The vector is

=

⟨

1

,

−

2

,

1

⟩

Explanation:

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

∣

∣

∣

∣

∣

→

i

→

j

→

k

d

e

f

g

h

i

∣

∣

∣

∣

∣

where

⟨

d

,

e

,

f

⟩

and

⟨

g

,

h

,

i

⟩

are the 2 vectors

Here, we have

→

a

=

⟨

2

,

3

,

4

⟩

and

→

b

=

⟨

1

,

2

,

3

⟩

Therefore,

∣

∣

∣

∣

∣

→

i

→

j

→

k

2

3

4

1

2

3

∣

∣

∣

∣

∣

=

→

i

∣

∣

∣

3

4

2

3

∣

∣

∣

−

→

j

∣

∣

∣

2

4

1

3

∣

∣

∣

+

→

k

∣

∣

∣

2

3

1

2

∣

∣

∣

=

→

i

(

3

⋅

3

−

2

⋅

4

)

−

→

j

(

2

⋅

3

−

1

⋅

4

)

+

→

k

(

2

⋅

2

−

3

⋅

1

)

=

⟨

1

,

−

2

,

1

⟩

=

→

c

Verification by doing 2 dot products

⟨

1

,

−

2

,

1

⟩

.

⟨

2

,

3

,

4

⟩

=

1

⋅

2

−

2

⋅

+

1

⋅

4

=

0

⟨

1

,

−

2

,

1

⟩

.

⟨

1

,

2

,

3

⟩

=

1

⋅

1

−

2

⋅

2

+

1

⋅

3

=

0

So,

→

c

is perpendicular to

→

a

and

→

b