Formula for collinear vectors

Condition of vectors collinearity 1. Two vectors a and b are collinear if there exists a number n such that

a = n · b

Condition of vectors collinearity 2. Two vectors are collinear if relations of their coordinates are equal.

N.B. Condition 2 is not valid if one of the components of the vector is zero.

Condition of vectors collinearity 3. Two vectors are collinear if their cross product is equal to the zero vector.

N.B. Condition 3 applies only to three-dimensional (spatial) problems.

The proof of the condition of collinearity 3

Let there are two collinear vectors a = {ax; ay; az} and b = {nax; nay; naz}. We find their cross product

a × b = ijk = i (aybz - azby) - j (axbz - azbx) + k (axby - aybx) =

ax ay az

bx by bz

= i (aynaz - aznay) - j (axnaz - aznax) + k (axnay - aynax) = 0i + 0j + 0k = 0

Examples of tasks

Examples of plane tasks

Example 1. Which of the vectors a = {1; 2}, b = {4; 8}, c = {5; 9} are collinear?

Solution: Since the vectors does not contain a components equal to zero, then use the condition of collinearity 2, which in the case of the plane problem for vectors a and b will view:

ax = ay.

bxby

Means:

Vectors a and b are collinear because 1 = 2.

48

Vectors a and с are not collinear because 1 ≠ 2.

59

Vectors с and b are not collinear because 5 ≠ 9.

48

Step-by-step explanation:

means if you're already damaged some way when you take out a medical insurance you will not get full compensation for that injury that you already have.

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*