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• Find the area of ​​a triangle constructed on vectors а‾ = ı‾ + ȷ‾ , ̅b‾=2ȷ‾.

Show that the points (-2,0), (2,3) and (5,-1) are the vertices of a right triangle. And find its area

Find the equation of the locus of the center of the circle which moves so that it is tangent to the y-axis and to the circle of radius one (1) with center at (2,0).

Given that a = 3i - 5j, determine the angle vector a makes with the positive x-axis b. Given that c = 5i + 3j, d = 3i – 2j. Find the magnitude of (i) c + d (ii) c – d

Find the direction cosine (l, m, n) of vector r = 3i -2j + 6k b. Given that p = -12 and q = 1. Find a unit vector u such that │u│= 35 and u is the direction of p-3q 5 -1

Determine the value of 𝑎 so that 𝑨 = 2𝒊 − 𝑎𝒋 + 𝒌 and 𝑩 = 4𝒊 − 2𝒋 − 2𝒌 are perpendicular.

Question text

An aeroplane flies at a ground velocity (i.e. velocity relative to

the ground) of 300 km/h N 30o W, in a wind blowing at a velocity

of 50 km/h N 20o E. What is the velocity (speed and direction)

of the plane relative to the ground? (Use a calculator and round the speed

to the nearest km/h, and the corresponding angle to the nearest degree.)

Water is flowing downhill at 15.0m/s through a pipe that is at an angle of 75° with the horizontal. What are the components of its velocity?

An aeroplane heads due north at 500km/h. It experiences a 80km/h cross wind flowing in the direction N60 degrees E

find the true velocity of the aeroplane

determine the died of the aeroplane.

Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. z^2=4+4r^2

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