Chapter 9: Q. 42 (page 627)

Find a vector orthogonal to both u and w.
$u = 2 i - 3 j + k w = i + j + 3 k$

Short Answer

Expert verified

The vector $10 i - 5 j + 5 k$ is orthogonal to both u and w

Step by step solution

Step1. Given information

vectors

$u = 2 i - 3 j + k w = i + j + 3 k$

According to geometrical properties of the cross, the product is the resultant of the cross product is orthogonal to both vectors

so orthogonal vector = $u \times w$

Step2. Calculating the orthogonal vector

$u = 2 i - 3 j + k w = i + j + 3 k u \times w = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ 1 & 1 & 3 \end{matrix}| u \times w = [i |\begin{matrix} - 3 & 1 \\ 1 & 3 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ 1 & 3 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ 1 & 1 \end{matrix}|] u \times w = - 10 i - 5 j + 5 k$

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Find a vector orthogonal to both u and w.
$u = 2 i - 3 j + k w = i + j + 3 k$

Short Answer

Step by step solution

Step1. Given information

Step2. Calculating the orthogonal vector

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Find a vector orthogonal to both u and w.u=2i-3j+kw=i+j+3k

Short Answer

Step by step solution

Step1. Given information

Step2. Calculating the orthogonal vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find a vector orthogonal to both u and w.
$u = 2 i - 3 j + k w = i + j + 3 k$