Chapter 9: Q. 41 (page 603)

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

Short Answer

Expert verified

The vector $- 9 i - 7 j - 3 k$ is orthogonal to both u and v

Step by step solution

Step1. Given information

vectors $u = 2 i - 3 j + k v = - 3 i + 3 j + 2 k$

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

so orthogonal vector = $u \times v$

Step2.Calculating the cross product

$u \times v = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ - 3 & 3 & 2 \end{matrix}| u \times v = i |\begin{matrix} - 3 \\ 3 & 2 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ - 3 & 2 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ - 3 & 3 \end{matrix}| u \times v = - 9 i - 7 j - 3 k$

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

Short Answer

Step by step solution

Step1. Given information

Step2.Calculating the cross product

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

Short Answer

Step by step solution

Step1. Given information

Step2.Calculating the cross product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Probability and Statistics

Decision Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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