2. Show that √²(¹) = 0 provided the distance r from a point P(x, y, z) to the origin is not equal to zero, i.e., r = √√x² + y² + z².

Evaluate the following: a) [P., A] where A =(P + P3 + P2) 2m

6. Given vectors Ã= 2â, + 4ây + 10â, and B = -5âp + âo – 3âz, find (a) Ã+ B at P(0, –2,5) , with o = 90° (b) ÷Ē (c) Ã× B (d) The angle between A and B at P (e) The scalar component of A along B at P

10) A certain vector in the xy plane has an x component of 4[m] and a y component of 10[m]. Without changing its length, the vector is rotated in the xy plane until its x component is doubled. Its new y component is about: A) 20 [m] B) 7.2 [m} C) 5.0 [m] D) 4.5 Įm] E) 2.2 [m]

3. Let a, b, n be integers, with n > 0. Prove that a = b (mod n) if and only if a² + b² = 2ab (mod n²).

What is the dot product of two vectors A = 2x + 4 y + 7z and B = -3x + 8y - 2 z where it is understood that A and B are 3 dimensional vectors, and x, y, and z are vectors of length 1 along the x, y, and z axes.      A scalar +12     A scalar +16     A vector perpendicular to both A and B     A vector 6x +32y -14z

ex1

2022, before 4: 06pm. Submit all assignments in my Assignment Box in the Division office. Question 1 oone Find the scalar and vector products of two vectors, (3î – 4j + 5k) and b = a = (2î + j - 3k). Question 2 Use the geometric definition of the cross product and the properties of the cross product to calculate the following: a) (k +j) × (k - i) b) (î + j) × î) × ĵ) c) (4î × (î + ĵ) Question 3 The following external forces are acting on a body: F1 = (10, 2,1)N at point P (4,0,0)cm , %3D F2 = (0,0,5)N at point P2 (1,-3,0)cm and

2. Let u, v, w and x be vectors. Classify the following expressions as being one of the following: vector, real number, meaningless. (a) (ux v) x (w x x), (b) (ux v). (w x x), (c) (ux v) (w xx), (d) u. (v x W),