Expert: Steve Holleran - 12/7/2007

Question
how to find magnitude and direction of vectors say the given problem is v=6i+6j how do i find the magnitude and vector?

Answer
Hi Cole,

Okay, you just want to diagram the vector on the xy-axis system.

Draw the 6i vector from the origin along the positive x-axis.  Then draw the 6j vector vertically up from the terminal point of the 6i vector.  Now draw the resultant vector back to the origin.

You now should have a right triangle with horizontal leg 6 and vertical leg 6.  You can use the Pythagorean theorem (or the shortcut for the 45-45-90 triangle) to find the hypotenuse is 6*sqrt(2) = 8.49

Also, for the direction angle (the angle the resultant makes with the x-axis), tan(theta) = 6/6 = 1 so
theta = tan^-1 (1) = 45 degrees.  But you sorta knew this from the right triangle.  If it was not an isosceles triangle, you would use this inverse tangent function to find the angle.

Steve