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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 = $[\begin{matrix} i & j & k \\ A x & A y & A z \\ B x & B y & B z \end{matrix}]$

03

Substitute the values

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

A x B = $|\begin{matrix} i & j & k \\ 1 & 1 & 0 \\ 1 & 0 & - 2 \end{matrix}|$

= 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

Find the inverse of the transformation $x^{'} = 2 x - 3 y, y^{'} = x + y$ , that is, find x, y in terms of $x^{'}, y^{'}$ .

Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.

$(\begin{matrix} 2 & 2 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & - 1 \end{matrix})$

Evaluate the determinants in Problems 1 to 6 by the methods shown in Example 4. Remember that the reason for doing this is not just to get the answer (your computer can give you that) but to learn how to manipulate determinants correctly. Check your answers by computer.

$| \begin{matrix} 5 & 17 & 3 \\ 2 & 4 & - 3 \\ 11 & 0 & 2 \end{matrix} |$

Find the symmetric equations $(5.6) o r (5.7)$ and the parametric equations $(5.8)$ of a line, and/or the equation $(5.10)$ of the plane satisfying the following given conditions.

Line through $(4, - 1, 3)$ and parallel to $i - 2 k$ .

Find the distance between the two given lines.

$\frac{x - 1}{2} = \frac{y + 2}{3} = \frac{2 z - 1}{4} and \frac{x + 2}{- 1} = \frac{2 - y}{2}, z = \frac{1}{2}$

See all solutions

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