Chapter 10: Q. 26 (page 824)

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$

Short Answer

Expert verified

The value of $(u \times v) \cdot w = (- 1, 20, 1) and u \cdot (v \times w) = (- 4, 23, 21)$

Step by step solution

Step 1. Given Information

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

We have to find the value of $(u \times v) \cdot w and u \cdot (v \times w)$

Step 2. Firstly finding the value of (u×v)·w

The cross product of $u \times v = \det [\begin{matrix} i & j & k \\ 2 & 1 & - 3 \\ 4 & 0 & 1 \end{matrix}]$

Now solving the cross product.

localid="1649405220352" $u \times v = ((1) (1) - (- 3) (0)) i + ((2) (1) - (- 3) (4)) j + ((2) (0) - (1) (4)) k u \times v = (1 - 0) i + (2 + 12) j + (0 - 4) k u \times v = 1 i + 14 j - 4 k$

Step 3. Now finding the value of (u×v)·w

Now the vectors of $u \times v is (1, 14, - 4)$

role="math" localid="1649405226967" $(u \times v) \cdot w = (1, 14, - 4) \cdot (- 2, 6, 5) (u \times v) \cdot w = {1 + (- 2), 14 + 6, (- 4) + 5} (u \times v) \cdot w = (1 - 2, 14 + 6, - 4 + 5) (u \times v) \cdot w = (- 1, 20, 1)$

Step 4. Firstly finding the value of v×w

The cross product of

$v \times w = \det [\begin{matrix} i & j & k \\ 4 & 0 & 1 \\ - 2 & 6 & 5 \end{matrix}]$

Now solving the cross product

role="math" localid="1649405232879" $v \times w = ((0) (5) - (1) (6)) i + ((4) (5) - (1) (- 2)) j + ((4) (6) - (0) (- 2)) k v \times w = (0 - 6) i + (20 + 2) j + (24 + 0) k v \times w = - 6 i + 22 j + 24 k$

Step 5. Now finding the value of u·(v×w)

The vectors of $v \times w is (- 6, 22, 24)$

u \cdot (v \times w) = (2, 1, - 3) \cdot (- 6, 22, 24) u \cdot (v \times w) = {2 + (- 6), 1 + 22, - 3 + 24} u \cdot (v \times w) = (- 4, 23, 21)

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In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of (u×v)·w

Step 3. Now finding the value of (u×v)·w

Step 4. Firstly finding the value of v×w

Step 5. Now finding the value of u·(v×w)

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In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)localid="1649405204459" role="math" (u×v)·wandu·(v×w)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly finding the value of (u×v)·w

Step 3. Now finding the value of (u×v)·w

Step 4. Firstly finding the value of v×w

Step 5. Now finding the value of u·(v×w)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Geometry

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Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$