Vectors into Unit Vector Form – Outschool

Vectors into Unit Vector Form Lesson

I. The Basics

When you’re drawing a vector in the x-y coordinate plane, you must consider its magnitude (length) and its direction (angle).

The vector above has a magnitude of 12 and a direction of 30 degrees north of east (start east and draw a 30-degree angle towards the north). This vector can be expressed in component form by finding the legs of the right triangle formed by the vector:

This is a 30-60-90 triangle. Use the ratios you learned in the 30-60-90 triangle lesson to find the missing side lengths. Divide the length of the hypotenuse by 2 to find the length of the short leg. Multiply the length of the short leg by the square root of 3 to find the length of the long leg.

This vector in component form is [latex]6sqrt{3}[/latex]i+ [latex]6[/latex]j.

II. Vectors in Word Problems

Example: An airplane is flying at a constant speed of 550 miles per hour headed 60 degrees south of east. Find a vector to represent the airplane’s velocity at this time.

Step 1: Draw a graph to represent this situation.

Step 2: Use a 30-60-90 triangle to find the component vectors. Divide the length of the hypotenuse by 2 to find the length of the short leg. Multiply the length of the short leg by the square root of 3 to find the length of the long leg.

The airplane’s velocity can be represented by the vector [latex]275[/latex]i – [latex]275sqrt{3}[/latex]j.