1. Find the algebraic vector _18 in ordered triplet notation and unit vector notation where _(2,-3,4) and #(0,-2,3)- 2. Find the magnitude of the vector v =-27 + 7-34 - 3. Given a = (-1,2-3), b = 27 -7 + 4, and 2=7+ 7 do the required operations: a) 2a -b + 38 b) 3(a + 2b) - 2(8 -2) 4. Given A(1,-2,3) , 8(-2,3,-4), and C(0,1,-1). find the coordinates of a point D(x, y,=) such that INCD Is a parallelogram. 5. The magnitudes of two vectors a and b are | a |=2 and | b /=3 respectively, and the angle between them is a = 60* Find the value of the dot product of these vectors. 6. Find the dot product of the vectors a and b where a = (1,-2,0) and b =i -2/ -k . 7. For what values of k are the vectors a = (6,3,-4) and 6 = (3,4,-2) a) perpendicular (orthogonal)? b) parallel (collinear)? 8. Find the angle between the vectors a and b where a = (1,-2-1) and 6 = -2/ +* . 9. A triangle is defined by three points _1(0,1,2), 8(10,2). and C(-1,2,0). Find the angles 24, 28, and ZC of this triangle. 10. Given the vector a = (2,-3,4) , find the scalar projection: a) of a onto the unit vector bj of a onto the vector i - } c) of a onto the vector b =-7 + 27 + A dj of the unit vector i onto the vector a 11. Given two vectors a = (0,1,-2) and b = (-1,0,3) , find: a) the vector projection of the vector a onto the vector b bj the vector projection of the vector b onto the vector a c) the vector projection of the vector a onto the unit vector d) the vector projection of the vector , onto the vector a 12. The magnitudes of two vectors a and b are |a |= 2 and | |=3 respectively, and the angle between them is 2= 609 . Find the magnitude of the cross product of these vectors