Calculus ( how to solve these questions) 2

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7nef

Mathematics

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hello,

I want someone can explain how to solve these questions step by step. And why did we choose this c

Thanks



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*1772. Alidterm 1 (B) estion 3. MULTIPLE CHOICE: select the correct answer (there is only one). (a) The straight line passing through the point P(-2,1,4) and parallel to the vector v=3i -- 2j is of parametric equations: x = -2+36 ; y=1 ; z=4-20 B. False A. True (b) The plane : x + y-22 = -1 and the line L: x= -5+2t ; y=1+41 ; 2=-2 +3t A. intersect B. are parallel Salv. 0 (-5 +26) + (1+46) 21-2 (c) The symmetric equations of the straight line passing through the point P(5,2,-1) and perpendicular to the plane of equation x +2y + 4z = 3 are: y-2 2+1 X-5 = 2 4 اما و کا A True B. False MATH 1324 - Midterm 1 (A) ANSWERS 2 Question 1. MULTIPLE CHOICE: select the correct answer there is only one). (a) The straight line passing through the point P(2,3,-1) and parallel to the vector v=5i - 4k is of parametric equations: x=2+5ti y = 3 i z=-1-41 A. True B. False (b) The symmetric equations of the straight line passing through the point P(1,2,-3) and perpendicular to the plane of equation x - 2y +32 = -4 are: y-2 Z+3 x-1 = 2 3 A. True B. False (c) The line L: x = 3 -2t ; y = 6+5t ; 2=2+36 and the plane 9: 2x + y - z=1 B. are parallel A. intersect Solve fume: 263–24) +(6.5k)-(2731) - 1
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Explanation & Answer

I'm done!😊 Here it is:

In Question 1:
a. Just change the parametric equations of the line into symmetric form (where the left-hand
side is t).
x = 2+5t
y=3

t = (x-2)/5

t = (y-3)/0

(we disregard the undefined fraction here; we'll just use this equation for comparison)
z = -1 -4t t = (z+1)/-4
Thus,
(x-2)/5 = (y-3)/0 = (z+1)/-4
The corresponding denominators of these equations will indicate the direction vector of the
line, which is or v = 5i - 4k, and the last term constants in the corresponding
numerators is a...


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