We can use vectors to create the vector equation of a line. In order to create the vector equation of a line we use the position vector of a point on the line and the direction vector of the line. In order to find the direction vector we need to understand addition and scalar multipli...
Find both the vector equation and the parametric equation of the line containing the points P=[1,2,-3] and Q=[3,-2,1] Solution: A vector tangent to the line is which is given by We can use either P or Q to express the vector equation for the line. If we use P , then th...
The vector equation of a line is r = a + tb.In this equation, “a” represents the vector position of some point that lies on the line, “b” represents a vector that gives the direction of the line, “r” represents the vector of any general point on the line and “t” represent...
Find a vector equation with parameter t for the line through the points (- 1, -7, -4) and (-6, 6, 2). r(t) =?. Find a vector equation with parameter t for the line through the points (-1,-7,-4) and (-14,7,3). Find a vector equation with par...
vector, parametric, symmetric equations of line in R3 and cross product equation. The Attempt at a Solution I obtained the direction vector for the line (L3) that intersects L1 and L2. It is [1,2,2]. And I let the point of intersection between L3 and L1 be: [x1,y1,z1]=[4,8-...
Answer to: Find a vector equation for the line through the point P = (3,4,1) and parallel to the vector 3 i - 3 j -3 k By signing up, you'll get...
Step by step video & image solution for Find the vector equation of a line which is parallel to the vector 2 hat i- hat j+3 hat k and which passes through the point (5, -2,4). Also reduce it to Cartesian form. by Maths experts to help you in doubts & scoring excellent marks ...
【题目】The vector equation of the line L is given by$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} - 3 \\ 0 \\ 8 \end{bmatrix} + t \begin{bmatrix} 4 \\ - 1 \\ - 3 \end{bmatrix} $$Show that A(5,-3,2) is the foot of the perpendicular ...
This leads us to the vector form for the equation of a line. As we have seen in the point–slope form, we can think of a line as a point on the line and a slope representing the direction of the line. The problem with using the slope is that it assumes the line is not vertical...
(a1, a2, 0) × (bl, b2, 0) = (0,0, a1b2 –a2b1) = (alb2 –a2b1)k where k is the unit vector in the z-direction. The magnitude of the vector product can be used to find the area of a parallelogram. 13. The vector equation of a line passing through two points a and...