Vector Dot & Cross Product

Find the dot product of <1, -2> and <3, 2>.

• 1
• <3, -4>
• <4, 0>
• -1

Tags

CCSS.HSN.VM.A.1

Find the angle between vectors <1,3> and <2,-5>.

• 40.24°
• 49.76°
• 139.76°
• 92.57°

Tags

CCSS.HSN.VM.A.1

CCSS.HSF.TF.B.7

Find the angle between the two vectors:

• -0.789
• 142.1
• 100
• 0.789

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.A.2

CCSS.HSG.SRT.D.11

Find the dot product of the given vectors:

• 92
• 0
• -92
• none of the above

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.A.2

CCSS.HSN.VM.A.3

How do you know if two vectors are orthogonal?

• Their sum is 0.
• The dot product is 1.
• The angle between them is 0°.
• The dot product is 0.

Tags

CCSS.HSN.VM.A.1

CCSS.HSG.CO.A.1

CCSS.HSG.GPE.B.5

Find the direction angle of the resulting force of the combined vectors given magnitude and direction:
F₁ : magnitude = 60 lbs, θ = 80°
F₂ : magnitude = 80 lbs, θ = 20°

• 121.66 lbs
• <85.6, 86.5>
• 45.3°
• 140 lbs

• -23i+7j-k

• 23i+7j-k

• -2i+j-7k

• -3i+7j-k

• i+8j+11k

• 8i+10j+11k

• i+10j-1k

• -i+2j+3k

• 11𝑖-13𝑗+3𝑘

• -11𝑖+13𝑗−3𝑘

• 1𝑖+13𝑗−3𝑘

• 11𝑖+13𝑗−3𝑘

• 382𝑖−136𝑗+158𝑘

• −382𝑖+136𝑗+158𝑘

• −382𝑖−136𝑗+158𝑘

• −82𝑖−13𝑗+158𝑘