Vector Analysis and Angle Calculation

The video tutorial explains how to find the magnitude and direction of a vector given in component form. It begins by sketching the vector in standard position, forming a right triangle on the coordinate plane. The magnitude is calculated using the Pythagorean theorem, and the direction is determined using the arctangent function. The tutorial also covers simplifying the magnitude by identifying perfect square factors. The direction is verified using a calculator in radian mode, ensuring the angle is within the specified interval.

What is the interval for the angle theta when measuring the direction of vector u?

• 0 to π radians

• 0 to 2π radians

• 0 to π/2 radians

• 0 to 3π radians

In standard position, where is the initial point of vector u located?

• At the terminal point

• At the origin

• At the midpoint

• At the endpoint

What geometric shape is formed when sketching the x and y components of vector u?

• A rectangle

• A circle

• A square

• A right triangle

Which theorem is used to calculate the magnitude of vector u?

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of calculus

• Remainder theorem

What is the simplified form of the magnitude of vector u?

• √26

• √52

• 4√13

• 2√13

How is the angle theta calculated for vector u?

• Using arctangent function

• Using cosine function

• Using secant function

• Using sine function

What is the ratio used in the arctangent function to find theta?

• y minus x

• y divided by x

• x divided by y

• x plus y

In which quadrant is the angle theta located for vector u?

• First quadrant

• Third quadrant

• Fourth quadrant

• Second quadrant

What mode should the calculator be in to find the angle in radians?

• Decimal mode

• Radian mode

• Gradient mode

• Degree mode

What is the rounded value of the angle theta in radians?

• 1.570 radians

• 0.785 radians

• 1.047 radians

• 0.588 radians