{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assign1_soln

# assign1_soln - Math 136 Assignment 1 Solutions 1 Compute...

This preview shows pages 1–2. Sign up to view the full content.

Math 136 Assignment 1 Solutions 1. Compute each of the following. a) (1 , 3 , 4) + ( - 1 , 1 , 2) Solution: (1 , 3 , 4) + ( - 1 , 1 , 2) = (0 , 4 , 6). b) 3( - 1 , 1 , - 2) - 2(2 , 0 , 3). Solution: 3( - 1 , 1 , - 2) - 2(2 , 0 , 3) = ( - 3 , 3 , - 6) + ( - 4 , 0 , - 6) = ( - 7 , 3 , - 12). 2. Determine the distance between P (2 , 1 , 1) and Q (1 , - 1 , 1). Solution: The distance is (1 , - 1 , 1) - (2 , 1 , 1) = ( - 1 , - 2 , 0) = ( - 1) 2 + ( - 2) 2 + 0 2 = 5. 3. Determine which of the following pairs of vectors is orthogonal. a) (2 , 1 , 1), ( - 2 , 1 , 3). Solution: We have (2 , 1 , 1) · ( - 2 , 1 , 3) = - 4 + 1 + 3 = 0 so they are orthogonal. b) ( - 1 , 3 , 6), (3 , - 1 , 0). Solution: We have ( - 1 , 3 , 6) · (3 , - 1 , 0) = - 3 - 3 + 0 = - 6 so they are not orthogonal. 4. Find an equation for the plane through P (3 , - 2 , 1) and parallel to x 1 - x 2 + 2 x 3 = 4. Solution: Since the plane is parallel to x 1 - x 2 + 2 x 3 = 4 it must have normal vector n = (1 , - 1 , 2). Thus the equation of the plane is x 1 - x 2 + 2 x 3 = 1(3) - 1( - 2) + 2(1) = 7 . 5. For each of the following sets: i) Determine if the set is linearly dependent or linearly independent. Justify. ii) Describe geometrically the span of the set and give a simplified vector equation which describes it.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}