.
Thank you for your question.
The condition that two vectors (a,b) and (c,d) in a coordinate plane are perpendicular is
that their scalar product (so called dot-product) a*c + b*d is equal to zero:
a*c + b*d = 0
In your case it means that
4*(k+3) = 2k.
You can easily solve this simple single linear equation
4k + 12 = 2k ====> 2k = - 12 ====> k = -6.
Solved.
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If you want to learn more on dot-product, look into my lessons in this site
- Introduction to dot-product
- Formula for Dot-product of vectors in a plane via the vectors components
- Dot-product of vectors in a coordinate plane and the angle between two vectors
- Perpendicular vectors in a coordinate plane
- Solved problems on Dot-product of vectors and the angle between two vectors
- Properties of Dot-product of vectors in a coordinate plane
- The formula for the angle between two vectors and the formula for cosines of the difference of two angles
There are short lessons of the "HOW TO . . . " type on Dot-product:
- HOW TO find dot-product of two vectors in a plane
- HOW TO find scalar product of two vectors in a coordinate plane
- HOW TO find the angle between two vectors in a coordinate plane
- HOW TO prove that two vectors in a coordinate plane are perpendicular
- HOW TO prove that a triangle in a coordinate plane is a right triangle
- HOW TO check if a quadrilateral in a coordinate plane is a parallelogram
- HOW TO check if a quadrilateral in a coordinate plane is a rectangle
- HOW TO check if a quadrilateral in a coordinate plane is a rhombus
- HOW TO check if a quadrilateral in a coordinate plane is a square
For the full list of my lessons on dot-product with short annotations see the file OVERVIEW of lessons on Dot-product.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Dot-product for vectors in a coordinate plane".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.