Scalar Product Challenge

Vector Coordinates

100

Find the coordinates of vector AB if A(1,2) and B(4,6)

(3,4)

200

Given A(-2,3) and B(1,-1), find the vector AB.

(3,-4)

300

Find the coordinates of vector BA if A(3,5) and B(-1,2)

(4,3)

400

Points A(2,-1), B(5,4) and C(1,3).
Find the sum of the vectors (AB + AC).

(2,9)

500

Point A(1,-2) and vector u(4,3). Find the coordinates of point B such as (vector AB)=(vector u)

B(5,1)

Magnitude of a Vector

100

Find the magnitude of vector (3,4)

5

200

Calculate the magnitude of the vector u, where u(-5,12)

13

300

Given A(1,2) and B(7,6). Find the length of the vector AB.

2 times radical 13

400

If v(2a,3a). Express the magnitude of v in terms of a. 

Radical of (13a²) 

500

Find the value of x such that the vector (x,4) has magnitude 5

x=3 or x=-3

Scalar Product

100

Compute the scalar product of (2,3) and (1,4)

14

200

Find the scalar product of u and v if u(-1,5) and v(3,2)

7

300

Let u(4,-2). Find u.u

20

400

Vectors u(x,2) and v(3,1). Find x if u.v=0

-2/3 

500

Two vectors have coordinates (a,1) and (2,a). Find all values of “a” such that their scalar product is 10. 

10/3

Cosine of an Angle

100

Write the formula for cos(a) between two vectors u and v.

cos(a)= (u.v)/(|u|.|v|)

200

Find cos(a) between the vectors (1,0) and (0,1).

Cos(a)=0

300

Vectors u(2,-1) and v(1,3). Calculate cos(a).

-1 over 5 radical 2 

400

Vectors u(2,1) and v(1,-2). Find the angle between them. 

90 degrees

True or False

200

u.v=v.u

True

300

Two vectors with the same magnitude are necessarily equal.

False

400

If cos(a)=-1, then the two vectors have opposite directions. 

True