Find the parametric equation of the line through a parallel to ba=[3−4],&nbsp;b=[−78]

Question

Find the parametric equation of the line through a parallel to ba=[3−4],&amp;nbsp;b=[−78]

Fommeirj · Accepted Answer

Step 1 The given vectors are a=[3−4], b=[−78] From the Eq. (3) the parametric vector equation of a line through a parallel to b is x=a+tb=[3−4]+t[−78] Hence, the equation is x=[3−4]+t[−78]

Luis Sullivan · Accepted Answer

Step 1  a=[3−4], b=[−78]  x=[3−4]+[−78]t  x1=3−7t  x2=−4+8t

Eliza Beth13 · Accepted Answer

To find the parametric equation of the line through a point parallel to a vector, let&#039;s consider the given vectors:a=[34] and b=[−78]We can observe that vector b is parallel to the desired line. To represent a line, we need a point on the line and its direction vector. We can choose point a as a point on the line and vector b as the direction vector.Let&#039;s denote the parametric equation of the line as:𝐫=𝐚+t𝐛where 𝐫 represents a position vector on the line, 𝐚 is the initial point on the line, t is a scalar parameter, and 𝐛 is the direction vector of the line.Substituting the values of 𝐚 and 𝐛 into the equation, we get:𝐫=[34]+t[−78]Expanding the equation, we have:𝐫=[3−7t4+8t]Therefore, the parametric equation of the line through point 𝐚 parallel to vector 𝐛 is:𝐫=[3−7t4+8t]

nick1337 · Accepted Answer

Answer:𝐫=[3−7t4+8t]Explanation:Let&#039;s consider the given vectors:a=[34] and b=[−78]We want to determine the equation of a line that passes through point a and is parallel to vector b.A general parametric equation for a line can be written as:𝐫=𝐚+t𝐯where 𝐫 represents a position vector on the line, 𝐚 is a known point on the line, t is a scalar parameter, and 𝐯 is the direction vector of the line.In this case, we can set 𝐚 as the given point a and 𝐯 as the given vector b. Substituting these values, we obtain:𝐫=[34]+t[−78]Simplifying, we get:𝐫=[3−7t4+8t]Hence, the parametric equation of the line passing through point a=[34] and parallel to vector b=[−78] is:𝐫=[3−7t4+8t]

madeleinejames20 · Accepted Answer

Given vectors a and b, we can observe that the direction vector of the line is the same as b. Therefore, 𝐫′(t), the derivative of 𝐫(t) with respect to t, will be equal to b.The vector equation of the line L can be written as:𝐫(t)=𝐚+t𝐛where 𝐚 is the initial point on the line and t is a parameter that determines different points on the line.Substituting the given values of a and b, we have:𝐫(t)=[34]+t[−78]Simplifying this equation, we get:𝐫(t)=[3−7t4+8t]Therefore, the parametric equation of the line L through a parallel to b is:𝐫(t)=[3−7t4+8t]

Find the parametric equation of the line through a parallel to ba=\begin

Answered question

Answer & Explanation

New Questions in Integral Calculus