19. Find the parametric vector equation of the line through egin{bmatrix} 1 \ 3 end{bmatrix} and egin{bmatrix} 4 \ 10 end{bmatrix}. Hint: what vector must we add to egin{bmatrix} 1 \ 3 end{bmatrix} to get egin{bmatrix} 4 \ 10 end{bmatrix}? 20. Suppose A is a 3 x 3 matrix with two pivot columns. (a) Does the equation Ax = 0 have a non-trivial solution? (b) Is the equation Ax = b consistent for every possible b?
Added by Isabella J.
Close
Step 1
Let's say the given point is $P_0(x_0, y_0, z_0)$ and the direction vector of the line is $\vec{d} = \begin{pmatrix} a \\ b \\ c \end{pmatrix}$. Then the parametric vector equation of the line can be written as: $\vec{r}(t) = \vec{P_0} + t\vec{d}$ where Show more…
Show all steps
Your feedback will help us improve your experience
Vishal Parmar and 54 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find: (a) A vector equation (b) Parametric equations (c) Symmetric equations of the line containing the point (1,2,3) and in the direction of $2 \mathbf{i}-\mathbf{j}+\mathbf{k}$.
Vectors; Lines, Planes, and Quadric Surfaces in Space
Equations of Lines and Planes in Space
Find parametric equations and an equation in vector form for the lines in R2 with the following equations: (a) y = 3x - 1 (b) 3x + 2y = 5
Hoan N.
Determine vector, parametric and, if possible, symmetric equations for the line through the point (-2, 2, 5) and parallel to the line through the points A(2, -3, 4) and B(3, 2, -1). Please solve using Grade 12 Calculus and Vectors Knowledge.
Shaiju T.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD