Find parametric equations for the line described below. The line through the poi

Question

Find parametric equations for the line described below. The line through the point P(-4, 1, -3) parallel to the vector 3i - 4j - 2k A) x = 3t + 4, y = -4t -1, z = -2t + 3 B) x = -3t + 4, y = 4t - 1, z = -2t + 3 C) x = 3t - 4, y = -4t + 1, z = -2t -3 D) x = -3t-4, y = -4t + 1, z = 2t - 3 The line through the point P(-3, 2, 7) and perpendicular to the vectors u = 8i - 2j - 8k and v = -8i + 2j + 5k A) x = 6t - 3, y = 24t + 2, z = -7t + 7 B) x = 6t - 3, y = -24t + 2, z = 0t + 7 C) x = 6t - 3, y = 24t + 2, z = 0t + 7 D) x = 6t + 3, y = 24t - 2, z = -7t - 7 Find a parametrization for the line segment joining the points. (-4, -6, -3), (0, -6, -5) A) x = -4t, y = -6t, z = 2t - 5, 0 lessthanorequalto t lessthanorequalto 1 B) x = -4t, y = -6, z = 2t - 5, 0 lessthanorequalto t lessthanorequalto 1 C) x = 4t - 4, y = -6t, z = -2t - 3, 0 lessthanorequalto t lessthanorequalto 1 D) x = 4t - 4, y = -6, z = -2t - 3, 0 lessthanorequalto t lessthanorequalto 1 Write the equation for the plane. The plane through the point P(3, 8, -7) and perpendicular to the line x = 5 + 8t, y = -5 + 3t z = 4 A) 8x + 3y + z = 55 B) 8x + 3y - z = -55 C) 8x + 3y - z = 4 D) 8x + 3y - z = 55

Explanation / Answer

12)

the line through the point P ( x1 , y1 , z1 ) and parallel to given vector ai + bj + ck is given by

( x - x1 ) / a = ( y -y1 ) / b = ( z - z1 ) / c

point = ( -4 , 1 , -3 )

vector = 3i - 4j - 2k

( x + 4 ) / 3 = ( y - 1 ) / -4 = ( z + 3 ) / -2

( x+ 4 ) / 3 = ( y -1 ) / -4 = ( z + 3 ) / -2

r(t) = (-4 , 1 , -3 ) + t ( 3 , -4 , -2 )

x = -4 + 3t

y = 1 - 4t

z = -3 - 2t

option C is correct

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