Three Dimensional Vector Operations - 3D Vector Operations Worksheet - Component Form and Magnitude Practice

Oct 8, 2026

Kuta Software-Infinite Precalculus worksheet focused on three-dimensional vectors, requiring learners to find component forms of resultant vectors and compute the magnitude of those results. Problems provide vectors such as f, u, g and sets labeled A, B, C, D as well as products like AB, CD, TX, and YZ. It emphasizes applying vector operations consistently across multiple examples to practice both coordinate-based results and overall length.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Find the component form of the resultant vector

Vector sums and products (AB, CD, TX, YZ)

Find the magnitude of the resultant vector

Vector magnitude calculations

Kuta Software-Infinite Precalculus Three Dimensional Vector Operations Name Date Period Find the component form of the resultant vector. 1) f 􀀠 􀀐􀀙 , 􀀐􀀛 , 􀀛 2) u 􀀠 􀀓 , 􀀜 , 􀀐􀀗 g 􀀠 􀀛 , 􀀐 􀀘 , 􀀖 g 􀀠 􀀜 , 􀀚 , 􀀐􀀚 Find: f 􀀎 g Find: u 􀀐 g 3) Given: A = (􀀐􀀙 , 􀀐􀀖 , 􀀐􀀘 ) B = (􀀐􀀗 , 􀀐􀀛 , 􀀘 ) 4) Given: T = (􀀐􀀕 􀀗 􀀐􀀔) X = (􀀖 􀀐􀀕 􀀐􀀘 ) C = (􀀐􀀕 , 􀀖 , 􀀐􀀗) D = (􀀐􀀙 , 􀀘 , 􀀓) Y = (􀀚 , 􀀘, , 􀀐, 􀀔) Z = (􀀚 , 􀀖,, 􀀐 􀀗, ) Find: 􀀐AB 􀀐 CD Find: TX 􀀎 YZ 5) a 􀀠 􀀔 , 􀀐􀀛 , 􀀘 6) u 􀀠 􀀐􀀕 , 􀀘 , 􀀐􀀙 g 􀀠 􀀐􀀙 , 􀀚 , 􀀐􀀚 g 􀀠 􀀐􀀕 , 􀀐􀀖 , 􀀛 Find: 􀀐 a 􀀐 􀀗g Find: 􀀗 u 􀀎 􀀔􀀓g 7) Given: A = (􀀐􀀙 , 􀀐􀀙 , 􀀐􀀗) B = (􀀗 , 􀀐􀀛 , 􀀚) 8) Given: P = (􀀓 􀀜 􀀚) Q = (􀀐􀀜 􀀐􀀗 􀀔) C = (􀀛 , 􀀜 , 􀀘 ) D = (􀀚 , 􀀕 , 􀀐􀀜) R = (􀀜,, 􀀐,􀀜 , 􀀐􀀗) S = ( 􀀐, 􀀛 , 􀀕, , 􀀓) Find: 􀀘AB 􀀎 􀀔􀀓 CD Find: 􀀙PQ 􀀐 􀀘RS Find the magnitude of the resultant vector. 9) f 􀀠 􀀐􀀜 , 􀀔 , 􀀐􀀚 10) f 􀀠 􀀘 , 􀀔 , 􀀓 v 􀀠 􀀗 , 􀀐 􀀔 , 􀀓 v 􀀠 􀀖 , 􀀚 , 􀀚 Find: f 􀀎 v Find: 􀀐 f 􀀎 v 11) Given: A = (􀀐􀀕 , 􀀖 , 􀀖) B = (􀀗 , 􀀐􀀜 , 􀀓) 12) Given: P = (􀀐􀀚 , 􀀚 , 􀀐􀀚 ) Q = (􀀔 , 􀀐􀀛 , 􀀐􀀜) C = (􀀘 , 􀀐􀀗 , 􀀕) D = (􀀛 , 􀀐􀀘 , 􀀔) R = (􀀐􀀚 , 􀀐􀀖 , 􀀘 ) S = (􀀐􀀖 , 􀀓 , 􀀓) Find: AB 􀀐 CD Find: 􀀐PQ 􀀐 RS 13) u 􀀠 􀀐􀀙 , 􀀐􀀚 , 􀀔 14) u 􀀠 􀀐􀀗 , 􀀐􀀗 , 􀀜 g 􀀠 􀀐􀀕 , 􀀕 , 􀀐􀀛 g 􀀠 􀀐􀀛 , 􀀗 , 􀀗 Find: 􀀐􀀖 u 􀀐 􀀔􀀓g Find: 􀀕 u 􀀎 􀀘 g 15) Given: A = (􀀛 , 􀀐􀀖 , 􀀜) B = (􀀐􀀘 , 􀀔 , 􀀙) 16) Given: T = (􀀐􀀖 􀀐􀀚 􀀐􀀙) X = (􀀖 􀀙 􀀐􀀔) C = (􀀐􀀗 , 􀀐􀀜 , 􀀘 ) D = (􀀐􀀛 , 􀀛 , 􀀐􀀕) Y = (􀀐􀀜 ,, 􀀐 􀀗 ,, 􀀐􀀜) Z = (􀀘 ,, 􀀔 ,, 􀀐􀀕) Find: 􀀐AB 􀀎 CD Find: 􀀙 TX 􀀎 􀀚YZ Kuta Software-Infinite Precalculus Three Dimensional Vector Operations Find the component form of the resultant vector. 1) f 􀀠 􀀐􀀙 , 􀀐􀀛 , 􀀛 g 􀀠 􀀛 , 􀀐 􀀘 , 􀀖 Find: f 􀀎 g 􀀕 , 􀀐􀀔􀀖 , 􀀔􀀔 3) Given: A = (􀀐􀀙 , 􀀐􀀖 , 􀀐􀀘 ) B = (􀀐􀀗 , 􀀐􀀛 , 􀀘 ) C = (􀀐􀀕 , 􀀖 , 􀀐􀀗) D = (􀀐􀀙 , 􀀘 , 􀀓) Find: 􀀐AB 􀀐 CD 􀀕 , 􀀖 , 􀀐􀀔􀀗 5) a 􀀠 􀀔 , 􀀐􀀛 , 􀀘 g 􀀠 􀀐􀀙 , 􀀚 , 􀀐􀀚 Find: 􀀐 a 􀀐 􀀗g 􀀕􀀖 , 􀀐􀀕􀀓 , 􀀕􀀖 7) Given: A = (􀀐􀀙 , 􀀐􀀙 , 􀀐􀀗) B = (􀀗 , 􀀐􀀛 , 􀀚) C = (􀀛 , 􀀜 , 􀀘 ) D = (􀀚 , 􀀕 , 􀀐􀀜) Find: 􀀘AB 􀀎 􀀔􀀓 CD 􀀗􀀓 , 􀀐􀀛􀀓 , 􀀐􀀛􀀘 Name Date Period 2) u 􀀠 􀀓 , 􀀜 , 􀀐􀀗 g 􀀠 􀀜 , 􀀚 , 􀀐􀀚 Find: u 􀀐 g 􀀐􀀜 , 􀀕 , 􀀖 4) Given: T = (􀀐􀀕 , 􀀗 , 􀀐􀀔) X = (􀀖 , 􀀐􀀕 , 􀀐􀀘 ) Y = (􀀚 , 􀀘 , 􀀐􀀔) Z = (􀀚 , 􀀖 , 􀀐􀀗) Find: TX 􀀎 YZ 􀀘 , 􀀐􀀛 , 􀀐􀀚 6) u 􀀠 􀀐􀀕 , 􀀘 , 􀀐􀀙 g 􀀠 􀀐􀀕 , 􀀐􀀖 , 􀀛 Find: 􀀗 u 􀀎 􀀔􀀓g 􀀐􀀕􀀛 , 􀀐􀀔􀀓 , 􀀘􀀙 8) Given: P = (􀀓 , 􀀜 , 􀀚) Q = (􀀐􀀜 , 􀀐􀀗 , 􀀔) R = (􀀜 , 􀀐􀀜 , 􀀐􀀗) S = (􀀐􀀛 , 􀀕 , 􀀓) Find: 􀀙PQ 􀀐 􀀘RS 􀀖􀀔 , 􀀐􀀔􀀖􀀖 , 􀀐􀀘􀀙 Find the magnitude of the resultant vector. 9) f 􀀠 􀀐􀀜 , 􀀔 , 􀀐􀀚 v 􀀠 􀀗 , 􀀐 􀀔 , 􀀓 Find: f 􀀎 v 􀀚􀀗 􀁼 􀀛􀀑􀀙􀀓􀀕 11) Given: A = (􀀐􀀕 , 􀀖 , 􀀖) B = (􀀗 , 􀀐􀀜 , 􀀓) C = (􀀘 , 􀀐􀀗 , 􀀕) D = (􀀛 , 􀀐􀀘 , 􀀔) Find: AB 􀀐 CD 􀀔􀀖􀀗 􀁼 􀀔􀀔􀀑􀀘􀀚􀀙 13) u 􀀠 􀀐􀀙 , 􀀐􀀚 , 􀀔 g 􀀠 􀀐􀀕 , 􀀕 , 􀀐􀀛 Find: 􀀐􀀖 u 􀀐 􀀔􀀓g 􀀚􀀖􀀚􀀗 􀁼 􀀛􀀘􀀑􀀛􀀚􀀕 15) Given: A = (􀀛 , 􀀐􀀖 , 􀀜) B = (􀀐􀀘 , 􀀔 , 􀀙) C = (􀀐􀀗 , 􀀐􀀜 , 􀀘 ) D = (􀀐􀀛 , 􀀛 , 􀀐􀀕) Find: 􀀐AB 􀀎 CD 􀀕􀀙􀀙 􀁼 􀀔􀀙􀀑􀀖􀀔 10) f 􀀠 􀀘 , 􀀔 , 􀀓 v 􀀠 􀀖 , 􀀚 , 􀀚 Find: 􀀐 f 􀀎 v 􀀛􀀜 􀁼 􀀜􀀑􀀗􀀖􀀗 12) Given: P = (􀀐􀀚 , 􀀚 , 􀀐􀀚 ) Q = (􀀔 , 􀀐􀀛 , 􀀐􀀜) R = (􀀐􀀚 , 􀀐􀀖 , 􀀘 ) S = (􀀐􀀖 , 􀀓 , 􀀓) Find: 􀀐PQ 􀀐 RS 􀀖􀀖􀀚 􀁼 􀀔􀀛􀀑􀀖􀀘􀀛 14) u 􀀠 􀀐􀀗 , 􀀐􀀗 , 􀀜 g 􀀠 􀀐􀀛 , 􀀗 , 􀀗 Find: 􀀕 u 􀀎 􀀘 g 􀀕 􀀜􀀚􀀖 􀁼 􀀙􀀕􀀑􀀖􀀛􀀙 16) Given: T = (􀀐􀀖 , 􀀐􀀚 , 􀀐􀀙) X = (􀀖 , 􀀙 , 􀀐􀀔) Y = (􀀐􀀜 , 􀀐 􀀗 , 􀀐􀀜) Z = (􀀘 , 􀀔 , 􀀐􀀕) Find: 􀀙 TX 􀀎 􀀚YZ 􀀖􀀙􀀜􀀙􀀙 􀁼 􀀔􀀜􀀕􀀑􀀕􀀙􀀘 Create your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

What skills does this worksheet practice for 3D vectors?

It practices finding the component form of resultant vectors and calculating the magnitude (length) of those resultant vectors.

How are resultant vectors formed in the problems?

Many items combine given vectors through operations like AB, CD, TX, YZ, or similar expressions, then ask for the resultant components.

What does the “magnitude of the resultant vector” section require?

It requires computing the length of the resultant vector formed from the specified vector operation(s), using the resultant’s components.

Oct 8, 2026

Uploaded by anakgang17