Chapter 9: Q. 45 (page 630)

In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
Find a unit vector orthogonal to both v and w.

Short Answer

Expert verified

The unit vector $3 i + 9 j + 9 k$ is orthogonal to bothvandw.

Step by step solution

Step 1. Given Information

The given vectors are $v = 3 i + j - 2 k a n d w = - 3 i + 2 j - k .$

Step 2. Finding the unit vector

By using the geometric property of the cross product, if uand vare vectors in space then $u \times v$ is orthogonal to both uand v.

So, to find the unit vector which is orthogonal to bothvandwlet's find the cross product.

Step 3. Solve

By using the formula of the cross product $v \times w = (b_{1} c_{2} - b_{2} c_{1}) i - (a_{1} c_{2} - a_{2} c_{1}) j + (a_{1} b_{2} - a_{2} b_{1}) k$

So, the unit vector is

$v \times w = (1 \cdot (- 1) - 2 \cdot (- 2)) i - (3 \cdot (- 1) - (- 3) \cdot (- 2)) j + (3 \cdot 2 - (- 3) \cdot 1) k v \times w = 3 i + 9 j + 9 k$

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In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
Find a unit vector orthogonal to both v and w.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the unit vector

Step 3. Solve

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In Problems 40–45, use the vectors v=3i+j-2kand w=-3i+2j-kto find each expression.Find a unit vector orthogonal to both v and w.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the unit vector

Step 3. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Discrete Mathematics

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
Find a unit vector orthogonal to both v and w.