If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)

a, b and c are three vectors in the third dimension with the following properties: a × b does not equal zero. a × b = b × c = c × a. Show that a + b + c = 0. Show that a + b + c = 0.

Let 03 = If possible, express w as a linear combination of the vectors 1, 02 and 3. Otherwise, enter DNE. For example, the answer w = 401+502+603 would be entered 4v1 + 5v2 + 6v3. w =

If possible express the vector v as a linear combination of V₁, V2, and V3.

If possible express the vector v as a linear combination of V₁, V2, and V3.

Consider the vectors , v = , and w=. Simplify the expressions on the left column and match its value on the right column. u = zu + v 2v - w w + (u + v) W zu (v - w) - U :: :: :: :: :: :: :: ::

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).

Let v= (4,5,8) and w=(-10,-8,9) be vectors. Find the scalar component of v in the direction of w. Also, write v as a sum of two vectors, one of which is parallel to w and the other of which is perpendicular to w.

Assume v₁ = [3,-2] and v₂ = [-1,4]. Find the sum and difference of vectors v₁ and v₂. V₁ + V₂ = [ V₁-V₂ = [ 1 1 de of the sum u +