Write a = 18 (0, 3, 0) as the sum of two vectors, one parallel and one perpendicular to b = If a = a +a, then: || (0,4,0) X (0, 4, 3).

For the given vectors u and v, find the cross product u x v. +- (²-₁-1-3) u x V = u = (-2, 6, 3), v =

For which a are the vectors ⟨2,a,1⟩ and ⟨1,−2,4⟩ perpendicular?

17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is the relationship between the two vectors for this result to be true? b) Determine the value(s) of k such that a + b < a + b. What is the relationship between the two vectors for this result to be true?

Determine whether the following three vectors lie on the same line in R3: и, 3 (4,6,8), и, - (2,3,4), и, 3(-2, -3, - 4), (The End)

What is î x (î × (î × (î + x)))? What is (x + ŷ) × ((& + ŷ) × )? Consider two vectors à and B. Write |Ã+ B| in terms of the length of Ā, the length of B, and the dot product of A and B.

Find two vectors Vy and V2 whose sum is (-5, –3), where 7y is parallel to (2, 5) while Uz is perpendicular to (2, 5).

For the vectors u = (-3,1) and v= proj, u = (-4,5), calculate proju and scalvu.

Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1, -1,2) * 12- Find the distance of the following vectors: (a – d)² + (2c - b) = a² * (b-d+c) =