VECTOR ALGEBRA

. $find\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}k$  

•  $\sqrt{22}$  

• 10

• 4

• 16

 $Find\ the\ angle\ between\ the\ vectors\ i-j+k\ and\ -i+j+2k$  

• 0

• 49.76°

• 90°

• 92.57°

 $Find\ the\ direction\ \cos ine\ of\ \ 3i-2j+3k$  Fin

•  $\frac{3}{22},\frac{-2}{22},\frac{3}{22}$  

•  $\frac{3}{\sqrt{22}},\frac{2}{\sqrt{22}},\frac{3}{\sqrt{22}}$  

•  $\frac{3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}}$  

•  $\frac{-3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}}$  

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

Tags

CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

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

• 3i + 3j - 3k

• 5i + 6j - 8k

• 6i + 9j -15k

• 6i + 6j - 15k

Tags

CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

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

Tags

CCSS.HSN.VM.A.2

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