Vector and scalar product

Question 1

scalar projection of a on b with included angle and mag

Answer 1

a.b=mag a x mag b x cos angle in between

Question 2

scalar projection

Answer 2

a.b/b.b
a.b/mag b^2

Question 3

unit vector in the direction of vector a

Answer 3

unit vector a=vector a/mag a

Question 4

Vector magnitude

Answer 4

Mag=square root of the i components^2 + j components^2

Question 5

scalar product of a on b in component form

Answer 5

a.b=X1xX2 + Y1xY2

Question 6

vector projection of a on b using scalar

Answer 6

u=a.b/b.b x vector b

Question 7

Vector projection of a onto by using unit vector b

Answer 7

u=(a.unit vector b) x unit vector b

Question 8

Finding the scalar projection - angle knowing mag of u

Answer 8

Mag of the vector projection. Cos Angle in between = mag u/mag a

Question 9

reaction of the plane

Answer 9

Tension that is perpendicular to the inclined plane

Question 10

Collinear
- show A, B, C to be collinear

Answer 10

Referred to when points lie on the same line. Show 2 of the lines to be parallel, have a point in common so therefore are collinear.

Question 11

Parallel lines

Answer 11

Are scalars of one another.

Question 12

a⋅(b+c)

Answer 12

=a⋅b+a⋅c

Question 13

(ka)⋅b

Answer 13

=k(a⋅b)=a⋅(kb)