Knowee
Questions
Features
Study Tools

Calculate the value of a for the points (1, 0, 1), (0, 1, 2), (-1, 2, a) and (7, 2, 1) so that theyare coplanar.

Question

Calculate the value of a for the points (1, 0, 1), (0, 1, 2), (-1, 2, a) and (7, 2, 1) so that they are coplanar.

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find the value of 'a' for the points to be coplanar, we can use the scalar triple product method. The points are coplanar if the scalar triple product of the vectors formed by these points is zero.

The vectors can be formed as follows:

Vector A = (0-1, 1-0, 2-1) = (-1, 1, 1) Vector B = (-1-1, 2-0, a-1) = (-2, 2, a-1) Vector C = (7-1, 2-0, 1-1) = (6, 2, 0)

The scalar triple product of A, B, and C is given by:

A.(BxC) = A. [(2, 2, a-1) x (6, 2, 0)] = A. [(20 - (a-1)2, (a-1)6 - 20, 26 - 22)] = A. [(-2a+2, 6a-6, 8)] = (-1, 1, 1).(-2a+2, 6a-6, 8) = -1*(-2a+2) + 1*(6a-6) + 1*8 = 2a - 2 + 6a - 6 + 8 = 8a - 0

For the points to be coplanar, A.(BxC) should be equal to 0.

So, 8a - 0 = 0 => 8a = 0 => a = 0/8 => a = 0

So, the value of 'a' for the points to be coplanar is 0.

This problem has been solved

Similar Questions

The points (3, −2, −1), (−1, 1, 2), (2, 3, −4) and (4, 5, λ) are coplanar when λ=

A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form.

find the coordinates of the points of trisection of line segment joining the points A(2,-2) and B(-7,4)

Determine whether the point (1, -3) lies on the line represented by the equation 2x + 3y = 7

Find a unit vector for a⃗ =<1,7>𝑎→=<1,7> in component form.Your final answer should have the denominator rationalized.

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.