Chapter 9: Q. 36 (page 627)

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k (u \times v) . w$

Short Answer

Expert verified

The required value of the expression is $- 25$ .

Step by step solution

Step 1. Given Information

We are given three vectors $u, v, w$ and we need to find the cross product of $(u \times v) . w$ .

Step 2. Finding cross product

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

The required cross product is

$u \times v = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ - 3 & 3 & 2 \end{matrix}| = i |\begin{matrix} - 3 & 1 \\ 3 & 2 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ - 3 & 2 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ - 3 & 3 \end{matrix}| = i ((- 3) . 2 - 3.1) - j (2.2 - (- 3) . 1) + k (2.3 - (- 3) . (- 3)) = - 9 i - 7 j - 3 k$

Step 3. Finding dot product

The required dot product is

$(u \times v) . w = (- 9 i - 7 j - 3 k) . (i + j + 3 k) = (- 9) . 1 + (- 7) . 1 + (- 3) . 3 = - 9 - 7 - 9 = - 25$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k (u \times v) . w$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding cross product

Step 3. Finding dot product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Use the given vectors u, v, and w to find each expression. u=2i-3j+k,v=-3i+3j+2k,w=i+j+3k(u×v).w

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding cross product

Step 3. Finding dot product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k (u \times v) . w$