• Wrong document? Swap it for free
  • Written by students who passed
  • Immediately available after payment
  • Read online or as PDF
  • 4.6 TrustPilot
0
Sell
Where do you study
Your language
Start selling Create your account
  • MATH 32A
  • MATH 32A
To add items to your wishlist, you must be logged in
Document preview thumbnail
Preview 2 out of 10 pages
Exam (elaborations)

MATH 32A Midterm 1 Exam | Questions and Solutions | 2026 Update | 100% Correct - UCLA

0.0
(0 reviews)
1 sold
10 pages
2025/2026 Written for academic year
Institution MATH 32A
Course MATH 32A
Document preview thumbnail
Preview 2 out of 10 pages

SECTION 1: TRUE/FALSE & VECTOR OPERATIONS (Question 1) Question 1 (8 points) Let u⃗,v⃗,w⃗u,v,w be vectors in R3R3. Answer True or False for each of the following statements. No justification is needed for this problem. (a) (2 points) If v⃗×w⃗=0⃗v×w=0, then either v⃗=0⃗v=0 or w⃗=0⃗w=0. (b) (2 points) If v⃗⋅w⃗=0v⋅w=0, then either v⃗=0⃗v=0 or w⃗=0⃗w=0. (c) (2 points) u⃗×(v⃗×w⃗)u×(v×w) makes sense. (d) (2 points) u⃗⋅(v⃗⋅w⃗)u⋅(v⋅w) makes sense. Solution: (a) False. The cross product of two nonzero vectors can be zero if they are parallel (collinear). For example, v⃗=⟨1,0,0⟩v=⟨1,0,0⟩ and w⃗=⟨2,0,0⟩w=⟨2,0,0⟩ are parallel, so v⃗×w⃗=0⃗v×w=0 but neither vector is zero. (b) False. The dot product can be zero for two nonzero vectors that are perpendicular (orthogonal). For example, v⃗=⟨1,0,0⟩v=⟨1,0,0⟩ and w⃗=⟨0,1,0⟩w=⟨0,1,0⟩ have dot product zero but neither is the zero vector. (c) True. The expression v⃗×w⃗v×w produces a vector, and taking the cross product of u⃗u with that vector is a valid vector operation. The result is a vector. (d) False. The expression v⃗⋅w⃗v⋅w produces a scalar (a number). Taking the dot product of u⃗u with a scalar is not defined; the dot product requires two vectors.

Content preview

MATH 32A Midterm 1 Exam | Questions and Solutions |
2026 Update | 100% Correct - UCLA

, MATH 32A Midterm 1 Examination (Winter 2025)
Below is a comprehensive Midterm 1 examination for MATH 32A - Calculus of
Several Variables. This exam covers topics from Chapters 13.1-13.5: vectors in the
plane and space, dot product, cross product, lines and planes in 3-space, and
vector functions .
Course: MATH 32A - Calculus of Several Variables
Exam: Midterm 1

Document information

Uploaded on
May 17, 2026
Number of pages
10
Written in
2025/2026
Type
Exam (elaborations)
Contains
Questions & answers
Report Copyright Violation
$25.49
Wrong document? Swap it for free Within 14 days of purchase and before downloading, you can choose a different document. You can simply spend the amount again.
Written by students who passed
Immediately available after payment
Read online or as PDF
Seller avatar
Reputation scores are based on the amount of documents a seller has sold for a fee and the reviews they have received for those documents. There are three levels: Bronze, Silver and Gold. The better the reputation, the more your can rely on the quality of the sellers work.
StudyVaultPro1
5.0
(2)
Sold
25
Followers
1
Items
3416
Last sold
1 day ago
Available in package deal
Product Image
Package deal
MATH 32A Package deal
-
-
Sold
3
item
Oct 2026
$74.67
$30.86
59% off More Info

Browse related subjects

Subjects

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

Student with book image

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Working on your references?

Create accurate citations in APA, MLA and Harvard with our free citation generator.

Learn more Create citation
Working on your references?

Frequently asked questions