1. Consider the vectors ū = (-1, 2), ở = (2,3) and w = (a, 3). (a) Find the resultant of ū and i, and check for which values of a it is parallel or perpen- dicular to w. (b) Give the unit vector in the direction of ū and calculate the angle between ữ and ū. (c) If A, B and C are points with position vectors ū, i and w (with respect to the origin (0,0,0)), respectively, find a point D so that [ABCD] gives a parallelogram (with vertices labelled clockwise). O =

Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

A:

Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

A:

Q: Find the magnitude only for the vector from T(-2, 6, 1) to U(10, -3, -4).

A:

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

A:

Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: Suppose (vector u)=(3,-4,-5) and Vector v=(2,-1,2)u+v=?u-v=?v-u=?3u=?(-1/4)v=?2u-3v=?I appreciate…

A: u=(3,-4,-5)v=(2,-1,2)

Q: Find the unit vector having the same direction as i = ( – 1,9). V82 V82, 9. of- 1 9. V82 V82 O (1,…

A: