Final answer:
The vector p = -i + 7j can be expressed in trigonometric form using its magnitude, which is 5√2, and its direction angle, which is greater than 90 degrees but less than 180 degrees due to its positioning in the second quadrant.
The correct answer is A.
Step-by-step explanation:
The given vector is p = -i + 7j. To convert this vector into trigonometric form, we need to calculate its magnitude and the angle it makes with the x-axis. The magnitude (r) of vector p is given by √((-1)^2 + (7)^2) = √(1 + 49) = √50 = √(25×2) = √25√2 = 5√2. Next, the angle (θ) with respect to the positive x-axis can be found using the arctan function, θ = arctan(7/-1).
This will give a negative value because the vector is in the second quadrant, so we add 180 degrees to find the correct angle in the standard position. Thus, the trigonometric form of vector p is 5√2[ cos(θ) + i sin(θ) ] where θ is greater than 90 degrees but less than 180 degrees.