Question

Consider the two vectors a with arrow = - ĵ and b with arrow = - - 2 ĵ. (a) Calculate a with arrow b with arrow. (b) Calculate a with arrow - b with arrow. (c) Calculate the directions of a with arrow b with arrow and a with arrow - b with arrow.

1) 0 -3 ĵ
2) 2 1 ĵ


5) a with arrow b with arrow ° (counterclockwise from the x axis)
6) a with arrow - b with arrow ° (counterclockwise from the x axis)

Answer 1

Vector algebra involves adding and subtracting vectors using the head-to-tail method and determining the magnitude and direction of the resultant vectors with a ruler and protractor.

Step-by-step explanation:

The question involves the algebra of vectors and calculating their sum and difference, as well as finding the direction of the resultant vectors. The process includes applying the head-to-tail method to combine vectors, and using a ruler and protractor to determine their magnitude and direction.

(a) To compute a with arrow + b with arrow, place the tail of b with arrow at the head of a with arrow. Draw the resultant vector from the tail of a with arrow to the head of b with arrow.

(b) To compute a with arrow - b with arrow, add the opposite vector of b with arrow (- b with arrow) to a with arrow using the head-to-tail method, then draw the resultant vector.

(c) Use a protractor to measure the angle of the resultant vectors counterclockwise from the x-axis to determine their directions.