Geometrically Vectors

Vector is a quantity with:

• magnitude and direction

• magnitude

• direction

• none of the above

• a is the position vector of point A

• b is the direction vector of line L

• r is the position vector of all points in L, represented by P(x,y)

• OB + BC = OC

• OA + AC = OC

• CB + B0 = -OC

• OD = 0.5(OA + AC)

Vectors a, b, c are defined as:

a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers

• a + b = 3i + 8j

• a - b = i + 8j

• a + c = -i + 4j

• c - b = -5i + 6j

Vector a = 2i + 3j - 5k. What is the value of 3a?

• 3i + 3j - 3k

• 5i + 6j - 8k

• 6i + 9j -15k

• 6i + 6j - 15k

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

• i + 3j -5k

• -i -3j +3k

• i -j -5k

• -i -j +3k

Given the vector v = 3i -2j +6 k, the magnitude of a is:

• 36

• 49

• 7

• 6

Given the line L: r = a + tb, where a = i+2j+3k and b= 2i -3j + k

• a line with direction vector 2i +4j + 6k is parallel to L

• a line with direction vector 4i -6j + 2k is parallel to L

• a line with direction vector 3i - j + 7k is parallel to L

Given points A(2, 1) and B(-4, 1). Explain why the vector AB is parallel to the x-axis

• because vector AB is a multiple of the unit vector i

• because vector AB is a multiple of the unit vector j

• because vector AB is a multiple of the unit vector k

Given parallel vectors u and v. Answer ALL that apply

• their scalar product is zero

• their scalar product is either 1 or -1

• u is a multiple of v

• magnitude of u equals the magnitude of v