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...
To find the vector equation of the line given in Cartesian form as (x+3)/2=(y−5)/4=(z+6)/2, we can follow these steps: Step 1: Identify the Direction RatiosFrom the given equation, we can identify the direction ratios of the line. The equation can be rewritten as:x+32=y...
【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 ...
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 ...
To find the vector equation of a line, you need a point on the line (P) and a direction vector (d). The vector equation is written as r = P + td, where t is a scalar variable. This equation can also be written as (x, y, z) = (x0, y0, z0) + t(a, b, c), where ...
Finding Vector Equation:Let us consider a line passing through the points A(−1,−7,−4), B(−6,6,2). And the line is parallel to direction vector v→=⟨a,b,c⟩. A vector equation of a line is defined by r→(t)=r0→(t)+tv→. For find...
Then the vector {eq}\mathbf{r}_1 -\mathbf{r}_0= \left<x_1-x_0, y_1-y_0,z_1-z_0\right> {/eq} is a direction vector that is parallel to the line segment, and a vector equation of the line segment is given by {eq}\mathbf{r}(t) = \mathbf{r}...
A line perpendicular to the given plane has the same direction as a normal vector to the plane. such as n=(1,3,1). So r_0= i+6 k, and we can take v= i+3 j+ k. Then a vector equation is r=( i+6 k)+t( i+3 j+ k)=(1+t) i+3t j+(6+t) k and parametric equa...
Given a vector-valued function defined by r(t)= ⎜t3+1t3+12t+1⎞⎠⎟r(t)=(t3+1t3+12t+1)Let TT denote the tangent to the curve at A=(2,2,3)A=(2,2,3).Then find the equation of the line LL passing through the point u=(1,−1,2)u=(1,−1,2),parallel...
【题】 V ector and parametric equations(a) Plot the vector equation r(t) = cos(t)i + si n(t)j; you may use a computer algebr a system ( e.g., Maple, Matlab, Wol fram Alp ha) to help you.(b) Write the parametric equations for the rect or equation r(t) = (2 + t)i ...