Q. 18 Compute the cross product of the... [FREE SOLUTION]

Chapter 11: Q. 18 (page 860)

Compute the cross product of the vector functions $r_{1} (t) = (x_{1} (t), y_{1} (t)) and (r_{2} (t) = x_{2} (t), y_{2} (t))$ by thinking of ${鈩�}^{2}$ as the xy-plane in ${鈩�}^{3} .$ That is, let $r_{1} (t) = (x_{1} (t), y_{1} (t), 0) and r_{2} (t) = (x_{2} (t), y_{2} (t), 0),$ and take the cross product of these vector functions.

Short Answer

Expert verified

The cross product of the given vector functions is $(x_{1} (t) y_{2} (t) - y_{1} (t) x_{2} (t)) k or (0, 0, x_{1} (t) y_{2} (t) - y_{1} (t) x_{2} (t)) .$

Step by step solution

Step 1. Given Information.

The given vector functions are $r_{1} (t) = (x_{1} (t), y_{1} (t), 0) and r_{2} (t) = (x_{2} (t), y_{2} (t), 0) .$

Step 2. Find the cross product.

Let's find the cross product of two vectors,

$= r_{1} (t) 脳 r_{2} (t) = |\begin{matrix} i & j & k \\ x_{1} (t) & y_{1} (t) & 0 \\ x_{2} (t) & y_{2} (t) & 0 \end{matrix}| = i [0] - j [0] + k [x_{1} (t) y_{2} (t) - y_{1} (t) x_{2} (t)] = (x_{1} (t) y_{2} (t) - y_{1} (t) x_{2} (t)) k$

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Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the cross product.

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91影视

Compute the cross product of the vector functions r1(t)=x1(t),y1(t)andr2(t)=x2(t),y2(t)by thinking of 鈩�2 as the xy-plane in 鈩�3.That is, let r1t=x1t,y1t,0andr2t=x2t,y2t,0,and take the cross product of these vector functions.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the cross product.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Decision Maths

Geometry

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.