Textbook Question
Given vectors u and v, find: 2u + 3v.
u = 2i, v = i + j
726
views
8. Vectors
Geometric Vectors
Problem 7.43c
Textbook Question
Given vectors u and v, find: v - 3u.
u = 〈-1, 2〉, v = 〈3, 0〉
Verified step by step guidance1
Identify the components of vector \( u \) as \( u = \langle -1, 2 \rangle \) and vector \( v \) as \( v = \langle 3, 0 \rangle \).
To find \( v - 3u \), first calculate \( 3u \) by multiplying each component of \( u \) by 3: \( 3u = 3 \times \langle -1, 2 \rangle = \langle 3 \times -1, 3 \times 2 \rangle \).
Simplify the expression for \( 3u \) to get \( 3u = \langle -3, 6 \rangle \).
Subtract \( 3u \) from \( v \) by subtracting the corresponding components: \( v - 3u = \langle 3, 0 \rangle - \langle -3, 6 \rangle \).
Perform the subtraction for each component: \( v - 3u = \langle 3 - (-3), 0 - 6 \rangle \).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vector Operations
Vector operations involve mathematical procedures applied to vectors, such as addition, subtraction, and scalar multiplication. In this case, we are performing a subtraction of a scaled vector from another vector. Understanding how to manipulate vectors is essential for solving problems involving them.
Recommended video:
04:12
Algebraic Operations on Vectors
Scalar Multiplication
Scalar multiplication is the process of multiplying a vector by a scalar (a single number), which scales the vector's magnitude without changing its direction. For example, multiplying vector u by -3 scales its components, affecting the resulting vector's position in the coordinate system.
Recommended video:
05:05Multiplying Vectors By Scalars
Coordinate Representation of Vectors
Vectors can be represented in a coordinate system using ordered pairs or tuples, such as u = 〈-1, 2〉 and v = 〈3, 0〉. Each component corresponds to a dimension in the space, allowing for geometric interpretation and algebraic manipulation of vectors in two-dimensional space.
Recommended video:
05:32Intro to Polar Coordinates
3:48mWatch next
Master Introduction to Vectors with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice