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1. Show that the plane given by -x+2z=0 and the line given by r(5, 2-t, 10+4t) are orthogonal,parallel or neither

2. State the equation and sketch the graph of the following: I.cylinder

II.elliptic paraboloid

III. hyperbolic paraboloid

IV.ellipsoid

3. Determine the equation of the plane containing the points P=(1, 3, 2), Q=(-2, 0, -2) and R=(1, 4, 3)

4. Write the equation of the line that passes through the points (2, -1, 3) and (1, 4, -3).

II. Write all three forms of the equation of the line.

5. Determine if the line that passes through the point (0, -3,8 ) and is 2t and is parallel to the line given by x=10+3t, y=12t and z=-3-t, passes through the xz-plane . If it does , give the coordinates of the point.

Only you ask 5five questions.

Slow down na

Answer na - 2.
Dont ask me how..

Uyi168:
Answer na - 2. Dont ask me how..

Hmm, let me ask how for asking sake

Waziced:
Only you ask 5five questions.
Slow down na

Na so mathematics be o

Question 1

The parametric equations of the line are
X = 5, y = 2 – t, z = 10 + 4t

--- From these equations, we know that a direction vector v of the line is v = (0, –1, 4).

--- This vector lies in the yz-plane while the plane –x + 2z = 0 is parallel to the y-axis, passes through the origin, and whose trace on xz-plane is the line r(t, 0, 2t).

--- Clearly, the line and the plane are neither parallel or perpendicular.

adebayo18015:
2. State the equation and sketch the graph of the following:
I.cylinder


II.elliptic paraboloid


III. hyperbolic paraboloid


IV.ellipsoid

NB: I can't supply the sketches. Just google them. The general equation of an ellipsoid is
x²/a + y²/b + z²/c = 1, a, b, and c are real numbers.

The equations of III, and IV really depend on the orientation of these quadric surfaces. Assuming they have the z-axis as their axis of orientation,
Elliptic paraboloid: z = x²/a + y²/b , a and b are real numbers
Hyperbolic paraboloid: z = x²/a – y²/b or z = y²/a – z²/b depending on the direction of the fold.

Any equation of a curve in a two-dimensional system involving any of the coordinate planes is a cylinder in the 3-dimensional coordinate system whose rulings are line normal to the coordinate plane and passes through the curve.

adebayo18015:
3. Determine the equation of the plane containing the points P=(1, 3, 2), Q=(-2, 0, -2) and R=(1, 4, 3)

A knowledge of Linear Algebra will be useful, especially that of the concept of a determinant. You need to form a 4 × 4 matrix using the coordinates of these points, four 1's and the x, y, and z variables. The equation of the line is –3x + 3y – 4z + 2 = 0.

adebayo18015:
4. Write the equation of the line that passes through the points (2, -1, 3) and (1, 4, -3).

II. Write all three forms of the equation of the line.

The parametric equations, using t as the parameter, of the line are
x = 1 – t, y = 4 + 5t, z = –3 – 6t

The symmetrical equations are
1 – x = (y – 4)/5 = (–3 – z)/6

Note that the parametric and symmetrical equations of a line in 3-space are not unique.

adebayo18015:
5. Determine if the line that passes through the point (0, -3,8 ) and is 2t and is parallel to the line given by x=10+3t, y=12t and z=-3-t, passes through the xz-plane . If it does , give the coordinates of the point.

I don't understand this.

Martinez39s:
A knowledge of Linear Algebra will be useful, especially that of the concept of a determinant. You need to form a 4 × 4 matrix using the coordinates of these points, four 1's and the x, y, and z variables. The equation of the line is –3x + 3y – 4z + 2 = 0.

Thanks for your time,but can you help shed more light on this

Martinez39s:
The parametric equations, using t as the parameter, of the line are
x = 1 – t, y = 4 + 5t, z = –3 – 6t

The symmetrical equations are
1 – x = (y – 4)/5 = (–3 – z)/6

Note that the parametric and symmetrical equations of a line in 3-space are not unique.

Am confused here sir

Martinez39s:
Question 1

The parametric equations of the line are
X = 5, y = 2 – t, z = 10 + 4t

--- From these equations, we know that a direction vector v of the line is v = (0, –1, 4).

- r(t, 0, 2t).

explain this please

adebayo18015:
Am confused here sir

There is nothing to be confused about. It's actually quite simple. You clearly haven't studied what I am talking about. Just read about it.