Geometrically Vectors

What is the magnitude of a vector geometrically?

• the length of the vector drawn

• the arrow head of the vector drawn

• The angle from the horizontal axis

• The angle from north

Find the magnitude of
vector AJ with A(0,-8,-7) and J(9,-2,-5). 
Write your answer in simplified form.

• 10

• 11

• 12

• 13

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

• 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)

A quantity that has both direction and magnitude, or size. It is represented by a coordinate plane.

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• preimage

• isometry

• vector

• OB + BC = OC

• OA + AC = OC

• CB + B0 = -OC

• OD = 0.5(OA + AC)

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

The scalar product of u and v is zero, therefore...

• vectors u and v are parallel

• vectors u and v are perpendicular

• vectors u and v are equal

• vectors u and v are multiples