Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.
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- Express the vector = + y. F 10 as a linear combination of -[-] and ÿ==A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t)=6ti−4tj+(9.8−4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up.(a) How high is the rooftop? meters.(b) When does the stone hit the ground? seconds.(c) Where does the stone hit the ground? (in meters)(d) How fast is the stone moving when it hits the ground? (in meters per second)Find a vector equation for the curve of intersectionof the surfaces x^2 + y^2 = 4 andz = xy.
- √a. = Find the length of the vector x = 3 -5 5 . Enter 'sqrt(a)' forFind both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5. Please explain your steps. Thank you.Calculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect
- A ball is thrown eastward into the air from the origin (in thedirection of the positive x-axis). The initial velocity is 50i+ 80k, with speedmeasured in feet per second. The spin of the ball results in a sounthwardacceleration of 4f t/s^2 , so the accelearation vector is a = −4j − 32k. Where does the ball land and with what speed?R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,Find the velocity, speed, and acceleration of a particle moving with position function r(t)=(3t^2-4)i+(3t)j Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t=2