Chapter 10: Q .13. (page 811)

Consider the position vector $i = 鉄� 1, 0, 0 鉄�$ in ${鈩�}^{3}$ Describe the set of position vectors $v$ in $ ${鈩�}^{3}$ with the property that $v 路 i = 0$ .

Short Answer

Expert verified

$The position vector should lie on y z -plane so that v 路 i = 0 holds.$

Step by step solution

Step 1:Given information

$i = 鉄� 1, 0, 0 鉄�$ in ${鈩�}^{3}$

Step 2:Explaination

$Consider the position vector i = 鉄� 1, 0, 0 鉄� in {鈩�}^{3}$

$Assume that the vector vin {鈩�}^{3} has the position vector v = 鉄� a, b, c 鉄� .$

$The dot product of v = 鉄� a, b, c 鉄� and i = 鉄� 1, 0, 0 鉄� is 0 .$

Therefore

$v 路 i = 0$

$鉄� a, b, c 鉄� 路鉄� 1, 0, 0 鉄� = 0 (Substitution)$

$1 a + 0 b + 0 c = 0 (Simplify)$

$1 a = 0$ ....equaton 1

$The equation (1) is satisfied for a = 0 .$

$The vector v in {鈩�}^{3} has the position vector v = 鉄� 0, b, c 鉄� so that v 路 i = 0 holds.$

$Thus, the position vector should lie on y z -plane so that v 路 i = 0 holds.$

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91影视

Consider the position vector $i = 鉄� 1, 0, 0 鉄�$ in ${鈩�}^{3}$ Describe the set of position vectors $v$ in $ ${鈩�}^{3}$ with the property that $v 路 i = 0$ .

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

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91影视

Consider the position vectori=鉄�1,0,0鉄�in 鈩�3Describe the set of position vectors vin $鈩�3with the property thatv路i=0.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Consider the position vector $i = 鉄� 1, 0, 0 鉄�$ in ${鈩�}^{3}$ Describe the set of position vectors $v$ in $ ${鈩�}^{3}$ with the property that $v 路 i = 0$ .