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प्रश्न
Show that the lines: `(1 - x)/2 = (y - 3)/4 = z/(-1)` and `(x - 4)/3 = (2y - 2)/(-4) = z - 1` are coplanar.
उत्तर
Given lines are: `(1 - x)/2 = (y - 3)/4 = z/(-1)` and `(x - 4)/3 = (2y - 2)/(-4) = z - 1`
or `(x - 1)/-2 = (y - 3)/4 = (z - 0)/1` and `(x - 4)/3 = (y - 1)/(-2) = (z - 1)/1`
There lines will be coplanar if `|(x_2 - x_1, y_2 - y_1,z_2 - z_1),(a_1, b_1, c_1),(a_2, b_2, c_2)|` = 0
`|(4 - 1, 1 - 3, 1 - 0),(-2, 4, -1),(3, -2, 1)| = |(3, -2, 1),(-2, 4, -1),(3, -2, 1)|` = 0 ...[Since, R1 = R3]
Thus, given lines are coplanar.
संबंधित प्रश्न
Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.
Show that four points A, B, C and D whose position vectors are
`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.
The lines `(x - 2)/(1) = (y - 3)/(1) = (z - 4)/(-k) and (x - 1)/k = (y - 4)/(2) = (z - 5)/(1)` are coplnar if ______.
If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______
If lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and x – 3 = `(y - k)/2` = z intersect then the value of k is ______.
If the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are coplanar, then ______.
If the straight lines `(x - 1)/2 = (y + 1)/k = z/2` and `(x + 1)/5 = (y + 1)/2 = z/k` are coplanar, then the plane(s) containing these two lines is/are ______.
Lines `overliner = (hati + hatj - hatk) + λ(2hati - 2hatj + hatk)` and `overliner = (4hati - 3hatj + 2hatk) + μ(hati - 2hatj + 2hatk)` are coplanar. Find the equation of the plane determined by them.
