Vector Magnitude and Direction Concepts

The video tutorial explains how to find the magnitude and direction of a vector given in component form. It starts by sketching the vector in standard position, then uses the Pythagorean theorem to calculate the magnitude. The direction is determined using trigonometry, specifically the arctangent function. The tutorial also covers simplifying the magnitude and using a calculator to find and verify the angle, ensuring it is in the correct quadrant.

What is the initial point of a vector in standard position?

• At the origin

• At the endpoint

• At the terminal point

• At the midpoint

How do you determine the terminal point of a vector with components (4, 6)?

• Move left 6 units and down 4 units

• Move left 4 units and down 6 units

• Move right 4 units and up 6 units

• Move right 6 units and up 4 units

Which theorem is used to find the magnitude of a vector?

• Remainder theorem

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

What is the formula for the magnitude of a vector with components (x, y)?

• x + y

• x^2 + y^2

• sqrt(x^2 + y^2)

• x^2 - y^2

How is the direction of a vector determined?

• Using the cosine function

• Using the sine function

• Using the cotangent function

• Using the tangent function

What is the range of the arctangent function?

• 0 to 180 degrees

• -180 to 180 degrees

• -90 to 90 degrees

• 0 to 360 degrees

What is the simplified form of the square root of 52?

• sqrt(52)

• sqrt(26)

• 4 sqrt(13)

• 2 sqrt(13)

What is the prime factorization of 52?

• 2 x 26

• 2 x 2 x 13

• 4 x 13

• 2 x 13

What should you ensure before using a calculator to find the angle?

• The calculator is in scientific mode

• The calculator is in degree mode

• The calculator is in radian mode

• The calculator is in standard mode

What is the approximate direction of vector u in degrees?

• 45.00 degrees

• 60.00 degrees

• 56.31 degrees

• 90.00 degrees