Consider line L, given below. x = 9 + t, y = 7 + t, z = 5 + 4t, t is in ℝ (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = Correct: Your answer is correct. v = Correct: Your answer is correct. (b) Find the distance from the origin to line L.

See the explanation.

Step-by-step explanation:

(a)

The equation of the line, L is given by x = 9 + t, y = 7 + t, z = 5 + 4t; where t is a real number.

In the above equation, if we put t = 0, then x = 9, y = 7 and z = 5.

Hence, the point (9, 7, 5) lies on the given line. We can say it as P.

The direction vector, v is {1, 1, 4}.

(b)

The equation of the given line can also be written as .

The vector, OP = (9, 7, 5), where O is the origin.

The direction vector v = {1, 1, 4}.

The cross product of OP and v is = {23, -31, 2}.

Hence, the distance is ≅9.

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.