The line through (1, -3, 4) that is parallel to the line r(t) = 3 + 4t, 5 - t, 7
ID: 2880614 • Letter: T
Question
The line through (1, -3, 4) that is parallel to the line r(t) = 3 + 4t, 5 - t, 7 The line through (0, 0, 0) that is perpendicular to both u = 1, 0, 2 and V = 0, 1, 1 The line through (-3, 4, 2) that is perpendicular to both u = left- 1, 1 -5 and v = left- 0, 4, 0 The line through (-2, 5, 3) that is perpendicular to both u = 4, 3, -5 and the z axis The line through (0, 2, 1) that is perpendicular to both u = 4, 3, -5 and the z-axis The line through (1, 2, 3) that is perpendicular to r _1 (t) = 3, -2t, 5 + 8t, 7 - 4t r _2(t) = -2t, 5 + t, 7 - t The line through (1, 0, -1) that is perpendicular to the lines r _1(t) = 3 + 2t, 3t, -4t and r _2(t) = t, t -tExplanation / Answer
Equation of line is given by r = a + tb, where a is the point through which it pases and b is its direction.
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18. A line through (1,-3,4) and parallel to (3+4t, 5-t,7)
r = a + tb,
a is the point through which it pases = (1,-3,4)and
b is its direction = (4,-1,0) ....( coefficient of t)
r= (1,-3,4) + t((4,-1,0)
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19. A line through ( 0,0,0) and perpendicular to u=<1,0,2>and v<0,1,1>
r = a + tb,
a is the point through which it pases = ( 0,0,0) and
b is its direction = cross product of u and v= (1 i + 0j + 2k) x ( 0i + 1j + 1k)= 1k -1j -2i= -2i -1j+1k
r= ( 0,0,0) + t(-2i -1j+1k )
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20. A line through (-3,4,2) and perpendidular to both u=<1,1,-5>and v=< 0,4,0>
r = a + tb,
a is the point through which it pases = (-3,4,2) and
b is its direction = cross product of u and v= (1i+1j-5k) x ( 0i+4j+0k)= 4k+20i= 20i + 4k
r= ( -3,4,2) + t(20i + 4k)
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21. A line through (-2,5,3) and perpendicular to both u=<1,1,2> and x-axis.
direction of x axis is (1,0,0)
r = a + tb,
a is the point through which it pases = (-2,5,3) and
b is its direction = cross product of u and v= (1i+1j+2k) x ( 1i+0j+0k)= 4k+20i= 20i + 4k
r= ( -2,5,3) + t(20i + 4k)
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