교과서 질문
In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°
899
views
Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer3rd EditionTrigonometryISBN: 9780137316601
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
TOC.tableOfContents
4장, 문제 53
In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. 4u - (2v - w)
검증된 단계별 안내1
Identify the given vectors: \( \mathbf{u} = -2\mathbf{i} + 3\mathbf{j} \), \( \mathbf{v} = 6\mathbf{i} - \mathbf{j} \), and \( \mathbf{w} = -3\mathbf{i} \).
Calculate \( 2\mathbf{v} \) by multiplying each component of \( \mathbf{v} \) by 2: \( 2\mathbf{v} = 2(6\mathbf{i} - \mathbf{j}) = 12\mathbf{i} - 2\mathbf{j} \).
Subtract \( \mathbf{w} \) from \( 2\mathbf{v} \): \( 2\mathbf{v} - \mathbf{w} = (12\mathbf{i} - 2\mathbf{j}) - (-3\mathbf{i}) = 12\mathbf{i} - 2\mathbf{j} + 3\mathbf{i} = 15\mathbf{i} - 2\mathbf{j} \).
Calculate \( 4\mathbf{u} \) by multiplying each component of \( \mathbf{u} \) by 4: \( 4\mathbf{u} = 4(-2\mathbf{i} + 3\mathbf{j}) = -8\mathbf{i} + 12\mathbf{j} \).
Subtract \( (2\mathbf{v} - \mathbf{w}) \) from \( 4\mathbf{u} \): \( 4\mathbf{u} - (2\mathbf{v} - \mathbf{w}) = (-8\mathbf{i} + 12\mathbf{j}) - (15\mathbf{i} - 2\mathbf{j}) = -8\mathbf{i} + 12\mathbf{j} - 15\mathbf{i} + 2\mathbf{j} = -23\mathbf{i} + 14\mathbf{j} \).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Vector Operations
Vector operations include addition, subtraction, and scalar multiplication. In this context, vectors are treated as quantities with both magnitude and direction, represented in component form. Understanding how to manipulate vectors through these operations is essential for solving problems involving multiple vectors.
추천 영상:
04:12
Algebraic Operations on Vectors
Scalar Multiplication
Scalar multiplication involves multiplying a vector by a scalar (a real number), which scales the vector's magnitude without changing its direction. For example, multiplying the vector u = -2i + 3j by a scalar 4 results in the vector -8i + 12j. This concept is crucial for transforming vectors in the given expression.
추천 영상:
05:05Multiplying Vectors By Scalars
Vector Subtraction
Vector subtraction is the process of finding the difference between two vectors, which can be visualized as adding the negative of one vector to another. For instance, subtracting vector w from 2v involves changing the direction of w and then adding it to 2v. This operation is key to simplifying the expression in the problem.
추천 영상:
05:29Adding Vectors Geometrically
관련 실천
교과서 질문
Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.
v = 2i - 8j
674
views
교과서 질문
In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = -10i + 15j
819
views
교과서 질문
Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.
||v|| = 10, θ = 330°
496
views
교과서 질문
In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. ||u + v||² - ||u - v||²
894
views
교과서 질문
In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 1/2, θ = 113°
892
views