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Chapter 10: Q .12 (page 811)

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

Short Answer

Expert verified

The position vector should lie ony-axis so thatv路i=0holds.

Step by step solution

01

Step 1:Given information

i=鉄�1,0鉄�in鈩�2

02

Step 2:Explaination

Consider the position vectori=鉄�1,0鉄�in鈩�2.

Assume that the vectorvin鈩�2has the position vectorv=鉄�a,b鉄�

The dot product ofv=鉄�a,b鉄�andi=鉄�1,0鉄�is0.

Therefore

v路i=0

鉄�a,b鉄�路鉄�1,0鉄�=0(Substitution)

1a+0b=0(Simplify)

1a=0Theequation(1)issatisfiedfora=0

The vectorvin鈩�2has the position vectorv=鉄�0,b鉄�so thatv路i=0holds.

Thus, the position vector should lie ony-axis so thatv路i=0holds.

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Most popular questions from this chapter

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(1,4,6),Q(鈭�3,5,0),R(3,2,鈭�1)

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=22,12,12

What is meant by the parallelogram determined by vectors u and v in 鈩�3? How do you find the area of this parallelogram?

What is the definition of the triple scalar product for vectors u, v and w in 鈩�3?

For each function f and value x = c in Exercises 35鈥�44, use a sequence of approximations to estimate f'(c). Illustrate your work with an appropriate sequence of graphs of secant lines.

role="math" localid="1648705352169" f(x)=ex,c=0
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