A vector has a magnitude of 2m, but is pointing in an unknown direction. What is the maximum possible magnitude of its horizontal component?

A vector has a magnitude of 50m and is pointing to the right, 30 degrees below the horizontal. What is the vertical component of this vector?

A vector has a horizontal component of 25m pointing right, and a vertical component of 30m pointing upwards. What is the direction of this vector, to the nearest degree?

how Sometimes, a component of a vector can be larger than the magnitude of the vector.

Find the vector with magnitude 5 and direction 𝜃 = ?M@ . Write your answer in 𝑣 = 𝑎𝒊 + 𝑏𝒋 form

Can the component of a vector ever be greater than the magnitude of the vector?Suppose you are working a physics problem that requires resolving a vectorinto its components. In many applications it is convenient to express the compo-nents in a coordinate system having axes that are not horizontal and vertical but arestill perpendicular to each other. If you choose reference axes or an angle otherthan the axes and angle shown in Figure 3.13, the components must be modifiedaccordingly. Suppose a vector B makes an angle
 with the x axis defined in Fig-ure 3.15. The components of B along the x and y axes are B x  B cos
 andBy  B sin
, as specified by Equations 3.8 and 3.9. The magnitude and directionof B are obtained from expressions equivalent to Equations 3.10 and 3.11. Thus,we can express the components of a vector in any coordinate system that is conve-nient for a particular situation