Chapter 10: Q .12 (page 811)

12. Consider the position vector $i = ⟨ 1, 0 ⟩$ in $ℝ^{2}$ . Describe the set of position vectors $v$ in $ℝ^{2}$ with the property that $v \cdot i = 0$ .

Short Answer

Expert verified

$The position vector should lie on y -axis so that v \cdot i = 0 holds.$

Step by step solution

Step 1:Given information

$i = ⟨ 1, 0 ⟩$ in $ℝ^{2}$

Step 2:Explaination

$Consider the position vector i = ⟨ 1, 0 ⟩ in ℝ^{2} .$

$Assume that the vector v in ℝ^{2} has the position vector v = ⟨ a, b ⟩$

$The dot product of v = ⟨ a, b ⟩ and i = ⟨ 1, 0 ⟩ is 0 .$

Therefore

$v \cdot i = 0$

$⟨ a, b ⟩ \cdot ⟨ 1, 0 ⟩ = 0 (Substitution)$

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

$1 a = 0$ $T h e e q u a t i o n (1) i s s a t i s f i e d f o r a = 0$

$The vector v in ℝ^{2} has the position vector v = ⟨ 0, b ⟩ so that v \cdot i = 0 holds.$

$Thus, the position vector should lie on y -axis so that v \cdot i = 0 holds.$

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12. Consider the position vector $i = ⟨ 1, 0 ⟩$ in $ℝ^{2}$ . Describe the set of position vectors $v$ in $ℝ^{2}$ with the property that $v \cdot i = 0$ .

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

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12. Consider the position vector i=⟨1,0⟩inℝ2. Describe the set of position vectors vin ℝ2with the property that v·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

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12. Consider the position vector $i = ⟨ 1, 0 ⟩$ in $ℝ^{2}$ . Describe the set of position vectors $v$ in $ℝ^{2}$ with the property that $v \cdot i = 0$ .