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Chapter 3: 20P (page 105)

Find a vector perpendicularto both i+j and i-2k .

Short Answer

Expert verified

The vector perpendicular to both the given vectors i+j and i-2k is -2i+2j-k .

Step by step solution

01

Given information

The given vectors are i+j and i-2k.

02

Formula used to find a vector perpendicular to the two vectors.

The formula used to find the vector perpendicular to the two vectors and is given by

A xB =ijkAxAyAzBxByBz

03

Substitute the values

Let the given vectors be A = i+j and B = i - 2k .

A x B = ijk11010-2

= i(-2-0) - j(-2-0) + k(0-1)

= i(-2) - j(-2) + k(-1)

= -2i+2j-k

Hence, the vector perpendicular to A = i+j and B = i-2k is .

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Most popular questions from this chapter

In Problems 19 to 22, solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3.

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For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using.

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