Question

how to find the magnitude of given two vectors

Answer 1

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The magnitude of a vector PQ−→− is the distance between the initial point P and the end point Q . In symbols the magnitude of PQ−→− is written as ∣∣∣ PQ−→− ∣∣∣ .

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Answer 2

Finding the Magnitude of a Vector at the Origin:-

• Determine the components of the vector. Every vector can be numerically represented in the Cartesian coordinate system with a horizontal (x-axis) and vertical (y-axis) component.

Example= the vector above has a horizontal component of 3 and a vertical component of -5, therefore the ordered pair is <3, -5>.

• Draw a vector triangle. When you draw the horizontal and vertical components, you end up with a right triangle. The magnitude of the vector is equal to the hypotenuse of the triangle so you can use the Pythagorean theorem to calculate it.

• Rearrange the Pythagorean theorem to calculate the magnitude. The Pythagorean theorem is A^2 + B^2 = C^2. “A” and “B” are the horizontal and vertical components of the triangle while “C” is the hypotenuse. Since the vector is the hypotenuse you want to solve for “C”.

x2 + y^2 = v^2

v = √(x^2 + y^2))

• Solve for the magnitude. Using the equation above, you can plug in the numbers of the ordered pair of the vector to solve for the magnitude.[4]
• For example, v = √((3^2+(-5)^2))
• v =√(9 + 25) = √34 = 5.831

• Don't worry if your answer is not a whole number. Vector magnitudes can be decimals.