Advertisements
Advertisements
Question
Find the vector equation of the line which passes through the point (3, 2, 1) and is parallel to the vector `2hat"i" + 2hat"j" - 3hat"k"`.
Solution
The vector equation of the line passing through A(`bar(a))` and parallel to the vector `bar"b"` is `bar"r" = bar"a" + lambdabar"b"`, where `lambda` is a scalar.
∴ the vector equation of the line passing through the point having position vector `3hat"i" + 2hat"j" + hat"k"` and parallel to the vector `2hat"i" + 2hat"j" - 3hat"k"` is `bar"r" = (3hat"i" + 2hat"j" + hat"k") + lambda(2hat"i" + 2hat"j" - 3hat"k")`.
APPEARS IN
RELATED QUESTIONS
Find the vector equation of the line passing through the point having position vector `-2hat"i" + hat"j" + hat"k" "and parallel to vector" 4hat"i" - hat"j" + 2hat"k"`.
Find the vector equation of the line passing through points having position vector `3hati + 4hatj - 7hatk and 6hati - hatj + hatk`.
Find the vector equation of line passing through the point having position vector `5hat"i" + 4hat"j" + 3hat"k"` and having direction ratios –3, 4, 2.
Find the cartesian equations of the line passing through A(–1, 2, 1) and having direction ratios 2, 3, 1.
Find the Cartesian equations of the line passing through A(2, 2, 1) and B(1, 3, 0).
Show that the lines given by `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1) and (x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/(4)` intersect. Also, find the coordinates of their point of intersection.
Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.
Find the vector equation of the plane which makes intercepts 1, 1, 1 on the co-ordinates axes.
Find the vector equation of the line which passes through the origin and the point (5, –2, 3).
Find the Cartesian equations of the line which passes through points (3, –2, –5) and (3, –2, 6).
Find the Cartesian equations of the line passing through the point A(1, 1, 2) and perpendicular to the vectors `barb = hati + 2hatj + hatk and barc = 3hati + 2hatj - hatk`.
Find the vector equation of the line which passes through the origin and intersect the line x – 1 = y – 2 = z – 3 at right angle.
If the lines `(x - 1)/(2) = (y + 1)/(3) = (z -1)/(4) and (x- 2)/(1) = (y +m)/(2) = (z - 2)/(1)` intersect each other, find m.
Find the vector and Cartesian equations of the line passing through the point (–1, –1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z − 2.
Find the Cartesian equation of the line passing through the origin which is perpendicular to x – 1 = y – 2 = z – 1 and intersect the line `(x - 1)/(2) = (y + 1)/(3) = (z - 1)/(4)`.
Find the vector equation of the line whose Cartesian equations are y = 2 and 4x – 3z + 5 = 0.
Find the coordinates of points on th line `(x - 1)/(1) = (y - 2)/(-2) = (z - 3)/(2)` which are at the distance 3 unit from the base point A(l, 2, 3).
Solve the following :
Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector `2hat"i" + hat"j" + 2hat"k"`.
Find the vector equation of the plane passing through the points A(1, -2, 1), B(2, -1, -3) and C(0, 1, 5).
Solve the following :
Find the cartesian equation of the plane passing through A(1,-2, 3) and direction ratios of whose normal are 0, 2, 0.
Solve the following :
The foot of the perpendicular drawn from the origin to a plane is M(1, 2, 0). Find the vector equation of the plane.
Solve the following :
A plane makes non zero intercepts a, b, c on the coordinate axes. Show that the vector equation of the plane is `bar"r".(bchat"i" + cahat"j" + abhat"k")` = abc.
Solve the following :
Find the vector equation of the plane passing through the origin and containing the line `bar"r" = (hat"i" + 4hat"j" + hat"k") + lambda(hat"i" + 2hat"j" + hat"k")`.
Find the Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)
Find the direction ratios of the line perpendicular to the lines
`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`
Reduce the equation `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8 to normal form
Find the Cartesian equation of the line passing through (−1, −1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z – 2
Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)
Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles
Find the Cartesian and vector equation of the line passing through the point having position vector `hat"i" + 2hat"j" + 3hat"k"` and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `2hat"i" - hat"j" + hat"k"`
The vector equation of the line passing through `4hati - hatj + 2hatk` and parallel to `-2hati - hatj + hatk` is ______
The equation of line is `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1`. The co-ordinates of the point on the line at a distance of 3 units from the point (1, -1, -1) is ______
Find the Cartesian equation of the plane passing through A(–1, 2, 3), the direction ratios of whose normal are 0, 2, 5.
Find the vector equation of the line passing through the points A(2, 3, –1) and B(5, 1, 2).
