Chapter 9: Q. 43 (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.
$v \times w$

Short Answer

Expert verified

The expression $v \times w = 3 i + 9 j + 9 k .$

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 given expression

To find the expression, substitute the values of vectors in the given expression.

Thus, $v \times w = (3 i + j - 2 k) \times (- 3 i + 2 j - k)$

Now, to find the cross product, use the definition of it.

If $v = a_{1} i + b_{1} j + c_{1} k$ and $w = a_{2} i + b_{2} j + c_{2} k$ are two vectors in space, the

cross product $v \times w$ is defined as the vector

$v \times w = (b_{1} c_{2} - b_{2} c_{1}) i - (a_{1} c_{2} - a_{2} c_{1}) j + (a_{1} b_{2} - a_{2} b_{1}) k$ .

Step 3. Solve

By proceeding with the calculation further using the formula of the cross product.

So,

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

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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.
$v \times w$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the given expression

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. v×w

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the given expression

Step 3. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Applied Mathematics

Geometry

Calculus

Statistics

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.
$v \times w$