Problem: Points A (0, 0, 0), B (2, \(-1\), 2) and C (3, 4, \(z\)) m are given. Find \(z\) so that the angle BAC is \(90^\circ\).
Making a Right Angle
ID: mdtsine9oo
Sources & References
Reference materials
1
Engineering Mechanics: Statics
R. C. Hibbeler
2021•Pearson
Ch. 2, §2.9 Dot Product
2
Vector Mechanics for Engineers: Statics
F. P. Beer, E. R. Johnston Jr., D. F. Mazurek
2019•McGraw-Hill Education
Ch. 3 "Rigid Bodies: Equivalent Systems of Forces", §3.2 Moment of a Force about an Axis
3
Engineering Mechanics: Statics
J. L. Meriam, L. G. Kraige, J. N. Bolton
2018•John Wiley & Sons
Ch. 2, Art. 2/7 Rectangular Components (Dot Product)
4
Engineering Mechanics: Statics
A. Bedford, W. Fowler
2004•Pearson Prentice Hall
Ch. 2, §2.5 Dot Products
5
Engineering Statics: Open and Interactive
D. W. Baker, W. Haynes
2026
Ch. 2, §2.7 Dot Products
Contributors
Community members
Content Editors
Keep learning
Notes, problems and apps on the same topics
Dot Product: Angle Between Vectors and Projection of a Force
Use the dot product to find the angle between two lines and the parallel and perpendicular components of a force.
0
1
0
0
0
0
Force Vector Directed Along a Line Using Position Vectors
Write a cable or rope force as a Cartesian vector from the coordinates of two points, using position and unit vectors.
0
0
0
0
0
0
Resolving a Force into Components Along Two Axes
Split a force into components along any two given directions, and see why oblique components are not projections.
0
0
0
0
0
0
Cartesian Vectors in 3D: Components and Direction Angles
Describe a force in 3D with i, j, k components, its magnitude, coordinate direction angles and unit vector.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Dot Product Visualizer: Angles and Projections in 3D
See what the dot product means: the angle between two directions and the part of a force along a line, drawn in 3D with its perpendicular part and a right-angle mark.
0
4
0
0
0
0
3D Force Vector Builder: Angles, Two Points and Sums
Build a force in space from its components, its three direction angles, two angles or two points, turn the 3D view with the mouse, and add several forces into one.
0
3
0
0
0
0
Moment and Torque Converter
Convert moments and torques between N·m, N·mm, kN·m, lbf·in, lbf·ft, kip·ft, kgf·m and more, with exact factors and the steps shown.
0
9
0
0
0
0
Force Resolver: Split a Force Along Any Two Directions
Split a force into two parts along any two directions, perpendicular or not, or into x and y parts from an angle or a slope, with every step shown on the drawing.
0
6
0
0
0
0
Introduction to Statics: Concepts, Principles and Units
Start statics here: its basic models and principles, SI and U.S. units, and a five-step method for solving problems, with practice problems and unit converters.
1
60
4
0
1
0
Report this comment to the editors
Editors can remove comments that break the rules.
Send feedback
Goes to the Hub 4 Mech Problem Team
About this problemMaking a Right AngleLog in to send feedback, so the team can answer you.
Comments 0
Discuss the solution, ask for a hint or share another approach to this problem.
Join the discussion
Log in to comment, reply and vote. It is free.
No comments yet
Ask a question, share a tip or say thanks. Be the first!