Given vectors u and v, find: v - 3u.
u = 2i, v = i + j

검증된 단계별 안내

Identify the given vectors: \( \mathbf{u} = 2\mathbf{i} \) and \( \mathbf{v} = \mathbf{i} + \mathbf{j} \).

Multiply vector \( \mathbf{u} \) by the scalar 3: calculate \( 3\mathbf{u} = 3 \times 2\mathbf{i} \).

Express \( 3\mathbf{u} \) in component form after multiplication.

Subtract \( 3\mathbf{u} \) from \( \mathbf{v} \) by subtracting corresponding components: \( \mathbf{v} - 3\mathbf{u} = (\mathbf{i} + \mathbf{j}) - (\text{components of } 3\mathbf{u}) \).

Write the resulting vector in terms of \( \mathbf{i} \) and \( \mathbf{j} \) components to complete the expression for \( \mathbf{v} - 3\mathbf{u} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Vector Representation in Component Form

Vectors can be expressed as sums of their components along the coordinate axes, typically using unit vectors i and j for the x and y directions. For example, u = 2i means the vector has a magnitude of 2 along the x-axis and zero along the y-axis.

Scalar Multiplication of Vectors

Scalar multiplication involves multiplying each component of a vector by a scalar value. For instance, multiplying vector u by 3 scales its magnitude by 3, resulting in 3u = 6i if u = 2i.

Vector Addition and Subtraction

Adding or subtracting vectors is done component-wise by combining their respective i and j components. To find v - 3u, subtract the components of 3u from those of v, resulting in a new vector.

Given vectors u and v, find: v - 3u. u = 2i, v = i + j