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1). Given the following vectors: u=(1, 2, -4) and v=(2, 3, 5)
Find:
a) u.v
b) u.u
c) (u.v) v
d) angle between u and v
e) unit vector
2. )Suppose that B =(2, 2, 1) and makes 30° with A and A•B = 6. What is the magnitude of A?
3. )What is the angle between A and B if A• B = 0
4.) Find (u+ v)•(2u – v) given that u•u= 4 u•v =-5 and v•v=10
5. )Determine if u and u = (cos 0, sin 0,–1); v=(sin 0,-cos 0,0) V are orthogonal
Definition, Formula and Physical interpretation of Collinear vector.
Definition, Formula and Physical interpretation of Cross Product.
A cable hangs in a parabolic arc between two poles 100 feet apart. The poles are 30 feet high and the lowest point on a suspended cable is 5 feet above the ground.
a) find the equation of the arc if the vertex is the lowest point of the cable
b) the opening of a cave 20 feet wide is in the shape of a semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center.
Find the slope-intercept form for the line perpendicular to 2x - 3y = -6 and passing through (4, 9)
Definition, Formula and Physical interpretation of Dot Product
A point moves so that the ratio of its distances from 3x + 4y + 8 = 0 and 4x + 3y – 6 = 0 is 2. Find the equation of its locus.
Let u = 2i – 3j + 4k v = 3i + k – 2k w = i+ 5j+3k
a. 2u + 3v + 4w
b. u . v and u . w
c. u x v and || u x v ||
d. Find the unit vector of u, v and w
e. Proj (u,w)
f. Establish the angle between the u and v.
Two forces act a point The magnitude of the Two forces are F, 2 newton and the measure of the angle between them is 60, if their resultant equal 2√3 newton,then F =newton
Use traces to sketch and identify the surface "x^2=y^2+4z^2"
