Question

q2 Let $u = \begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}$ and $v = \begin{bmatrix} 3 \\ 6 \\ 6 \end{bmatrix}$ be position vectors of points U and V, a. Write down the vector equation of a line passing through points U and V. b. Find the equations of the plane with normal $n = \begin{bmatrix} 1 \\ 2 \\ 6 \end{bmatrix}$ and having point U lying on it. c.Using the results of a), find the intersection between the line and the plane.

          q2
Let $u = \begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}$ and $v = \begin{bmatrix} 3 \\ 6 \\ 6 \end{bmatrix}$ be position vectors of points U and V,
a. Write down the vector equation of a line
passing through points U and V.
b. Find the equations of the plane with normal
$n = \begin{bmatrix} 1 \\ 2 \\ 6 \end{bmatrix}$ and having point U lying on it.
c.Using the results of a), find the
intersection between the line and the plane.

q2
Let u =
< b m a t r i x > and v =
< b m a t r i x > be position vectors of points U and V,
a. Write down the vector equation of a line
passing through points U and V.
b. Find the equations of the plane with normal
n =
< b m a t r i x > and having point U lying on it.
c.Using the results of a), find the
intersection between the line and the plane.

Added by Christine B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Dr Harish Viswanathan

Step 1

The vector equation of a line passing through points U and V can be written as: r = u + t(v - u) where r is the position vector of any point on the line, t is a scalar parameter, u is the position vector of point U, and v is the position vector of point V. So, Show more…

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Let u = [1, 1, 2] and v = [3, 6, 6]T be position vectors of points U and V. a. Write down the vector equation of a line passing through points U and V. b. Find the equations of the plane with normal n = [1, 2, 6] and having point U lying on it. c. Using the results of a), find the intersection between the line and the plane.