## Related questions with answers

Question

Find the real values of k for which the given vectors are orthogonal. If there are no such values, show why.

$\left[\begin{array}{l} {k} \\ {0} \\ {k^{2}} \end{array}\right],\left[\begin{array}{l} {1} \\ {2} \\ {3} \end{array}\right]$

Solution

VerifiedStep 1

1 of 2Two vectors are orthogonal if their scalar product is zero:

$\begin{bmatrix} k & 0 & k^2 \end{bmatrix} \cdot\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} =(k)(1)+(0)(2)+(k^2)(3)=k+3k^2=k(1+3k)=0$

Thus we then obtain $k=0$ or $1+3k=0$ which is equivalent with $3k=-1$ or $k=-\dfrac{1}{3}$.

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Differential Equations and Linear Algebra

2nd Edition•ISBN: 9780131860612 (1 more)Beverly H. West, Hall, Jean Marie McDill, Jerry Farlow2,405 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780134497181 (3 more)C. Henry Edwards, David Calvis, David E. Penney2,531 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780321964670Scott A. Annin, Stephen W. Goode3,457 solutions

#### Linear Algebra and Differential Equations (Custom Edition for University of California, Berkeley)

2nd Edition•ISBN: 9781256873211David C. Lay, Nagle, Saff, Snider2,362 solutions

## More related questions

1/4

1/7