Vectors

Question 1

How to prove two vectors are perpendicular to each other

Answer 1

If the dot product of the vectors equals zero
a . b = 0

Question 2

How to prove two vectors are parallel to each other

Answer 2

If the cross product of the vectors equals zero
a x b = 0

Question 3

Dot Product
a . b =

Answer 3

|a||b| cos θ

(ax bx + ay by + az bz)

Question 4

Cross Product
a x b =

Answer 4

|a||b| sin θ n
|a x b| = |a||b| sin θ

i (aybz- azby) - j (axbz - azbx) + k (axby - aybx)

Question 5

Scalar Triple Product
(a x b) . c =

Answer 5

(aybz - azby) cx + (azbx - axbz) cy + (axby - aybx) cz

used to calculate volume

| cx cy cz |

ax ay az |
|bx by bz |

Question 6

What is cross product also known as

Answer 6

Vector Product

Question 7

How do you prove vectors are coplanar to each other

Answer 7

If the scalar product of the vectors equals zero
(a x b) . c = 0

Question 8

What is dot product also known as

Answer 8

Scalar Product

Question 9

Express a vector in the Cartesian form

Answer 9

vector = i + j + k

Question 10

Express a vector in the row vector notation

Answer 10

vector = (x, y, z)

Question 11

Calculate the unit vector of x in the direction R

Answer 11

R

R = resultant force