Question 1112739
.
<pre>
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.
</pre>

Solved.


------------------
If you want to learn more on dot-product, look into my lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Introduction-to-dot-product.lesson>Introduction to dot-product</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Formula-for-Dot-product-of-vectors-in-a-plane-via-the-vectors-components.lesson>Formula for Dot-product of vectors in a plane via the vectors components</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Dot-product-of-vectors-in-a-plane-and-the-angle-between-two-vectors.lesson>Dot-product of vectors in a coordinate plane and the angle between two vectors</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Perpendicular-vectors-in-a-coordinate-plane.lesson>Perpendicular vectors in a coordinate plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-Dot-product-of-vectors-and-the-angle-between-two-vectors.lesson>Solved problems on Dot-product of vectors and the angle between two vectors</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Properties-of-Dot-product-of-vectors-in-a-coordinate-plane.lesson>Properties of Dot-product of vectors in a coordinate plane</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/The-formula-for-the-angle-between-two-vectors-and-the-formula-of-cosines-of-the-difference-of-two-angles.lesson>The formula for the angle between two vectors and the formula for cosines of the difference of two angles</A>


There are short lessons of the &nbsp;"<B>HOW TO . . . </B>"&nbsp; type on Dot-product:

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-dot-product-of-two-vectors-in-a-plane.lesson>HOW TO find dot-product of two vectors in a plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-scalar-product-of-two-vectors-in-a-coordinate-plane.lesson>HOW TO find scalar product of two vectors in a coordinate plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-the-angle-between-two-vectors-in-a-coordinate-plane.lesson>HOW TO find the angle between two vectors in a coordinate plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-prove-that-two-vectors-in-a-coordinate-plane-are-perpendicular.lesson>HOW TO prove that two vectors in a coordinate plane are perpendicular</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-prove-that-a-triangle-in-a-coordinate-plane-is-a-right-triangle.lesson>HOW TO prove that a triangle in a coordinate plane is a right triangle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-prove-that-a-quadrilateral-in-a-coordinate-plane-is-a-parallelogram.lesson>HOW TO check if a quadrilateral in a coordinate plane is a parallelogram</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-check-if-a-quadrilateral-in-a-coordinate-plane-is-a-rectangle.lesson>HOW TO check if a quadrilateral in a coordinate plane is a rectangle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-check-if-a-quadrilateral-in-a-coordinate-plane-is-a-rhombus.lesson>HOW TO check if a quadrilateral in a coordinate plane is a rhombus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-check-if-a-quadrilateral-in-a-coordinate-plane-is-a-square.lesson>HOW TO check if a quadrilateral in a coordinate plane is a square</A>


For the full list of my lessons on dot-product with short annotations see the file &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Vectors/REVIEW-of-the-lessons-on-Dot-product.lesson>OVERVIEW of lessons on Dot-product</A>. 


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Dot-product for vectors in a coordinate plane</U>".



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.