SOLUTION: The vectors are shown as the x and y on top of each other but since I can’t type it out like that, it’ll be separated with commas The vectors a = (4,2) and b = ( k + 3, k ) are pe

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Question 1112739: The vectors are shown as the x and y on top of each other but since I can’t type it out like that, it’ll be separated with commas
The vectors a = (4,2) and b = ( k + 3, k ) are perpendicular to each other. Find the value of k.

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
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.

------------------
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.


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