Chapter 10: Q .14. (page 811)

Consider the position vector $i = 鉄� 1, 0 鉄�$ in ${鈩�}^{2}$ . Describe the set of position vectors $v$ in ${鈩�}^{2}$ with the property that ${proj}_{i} v = i$ .

Short Answer

Expert verified

$Any position vector of the type v = 鉄� 1, b 鉄� {satisfies the conditionproj}_{i} v = i .$

Step by step solution

Step 1:Given information

the position vector $i = <1, 0>$ in ${鈩�}^{2}$

Step 2:Simplification

$Consider the position vector i = 鉄� 1, 0 鉄� in {鈩�}^{2} .$

$The vector projection of v onto u is given by:$

${proj}_{u} v = \frac{u 路 v}{鈥� u {鈥�}^{2}} u$

$Assume the position vectors of v = 鉄� a, b 鉄� and {proj}_{i} v = i .$

Therefore

${proj}_{i} v = i (Given condition)$

$\frac{1 路 v}{鈥� i {鈥�}^{2}} i = i (Substitution)$

$\frac{鉄� 1, 0 鉄� 路鉄� a, b 鉄�}{(1^{2} + 0^{2})} i = i (Simplify)$

$1 a = 1$

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

$The vector v in {鈩�}^{3} has the position vector v = 鉄� 1, b 鉄� so that proji v = i holds.$

$Thus, any position vector of the type v = 鉄� 1, b 鉄� {satisfies the conditionproj}_{i} v = i .$

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91影视

Consider the position vector $i = 鉄� 1, 0 鉄�$ in ${鈩�}^{2}$ . Describe the set of position vectors $v$ in ${鈩�}^{2}$ with the property that ${proj}_{i} v = i$ .

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

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91影视

Consider the position vector i=鉄�1,0鉄�in 鈩�2. Describe the set of position vectors vin 鈩�2with the property thatprojiv=i.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Consider the position vector $i = 鉄� 1, 0 鉄�$ in ${鈩�}^{2}$ . Describe the set of position vectors $v$ in ${鈩�}^{2}$ with the property that ${proj}_{i} v = i$ .