8) Find the unit tangenit vector TilE) at the poin Let ř(t)= <-5t'+3, Be -S sin (E)) 3t -3t -5cos (E)) 4. K-25€ -3t -9e 412 +(-969 + (-Scos (t) -3ti2
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Given curve
We need to find tangent vector .
Tangent vector is given by:
.
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Solved in 2 steps
- Find parametric and vector equation for line segment which reach (2, 2.4 , 3.5) point and parallel to the 3i + 2j -k vector a) (1+3t)i + (4+2t)j + (3-t)k b) (2+3t)i + (2.4+2t)j + (3.5-t)k c) (1+3t)i + (2+t)j - (3.5-2t)k d) (2t)i + (1.5-2t)j + (3.5-1t)kWe have to find parametric equation for a line that is tangent (intersection) of the two fields below: −2x + 3y + 7z = −2 and x + 2y - 3z = −5.Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to the vector 2i - j + k.
- Give a vector parametric equation for the line through the point (−4,2) that is perpendicular to the line ⟨−2, 4−3t⟩.Suppose L(5, 4) was reflected across the line y = x then translated along the vector <4, 0>. What is the y-coordinate of L''?I have attached an image of my problem and I got the vector equation values correct, but not the bounds. I got the bounds to be: 0<=t<=1, but the correct answer is supposed to be from -infinity to positive infinity (all values.) Is this because the line is just passing through the line segment and therefore the values are not restricted to those points on the line segment?
- Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection, determine the vector that specifies the velocity at which the pathogen is evolving directly away from the origin. (Hint: Your final answer will be a vector in the direction of the dashed line from the graphic and will involve k and θ)The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by the alpha angle and at the same time rotated in the positive xy direction by the beta angle, how is the new vector defined?