Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let A be the point whose position vector is a = `5hat"i" + 4hat"j" + 3hat"k"`.
Let `bar"b"` be the vector parallel to the line having direction ratio = –3, 4, 2
Then, `bar"b" = -3hat"i" + 4hat"j" + 2hat"k"`
The vector equation of the line passing through `"A"(bara)` and parallel to `bar"b" "is" bar"r" = bar"a" + lambdabar"b"`, where λ is a scalar.
∴ The required vector equation of the line is `bar"r" = 5hat"i" + 4hat"j" + 3hat"k" + lambda(-3hat"i" + 4hat"j" + 2hat"k").`
APPEARS IN
संबंधित प्रश्न
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 the line passing through the point having position vector `-hat"i" - hat"j" + 2hat"k" "and parallel to the line" bar"r" = (hat"i" + 2hat"j" + 3hat"k") + λ(3hat"i" + 2hat"j" + hat"k").`
Find the cartesian equations of the line passing through A(–1, 2, 1) and having direction ratios 2, 3, 1.
Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.
Find the Cartesian equation of the plane passing through A(7, 8, 6) and parallel to the XY plane.
The foot of the perpendicular drawn from the origin to a plane is M(1,0,0). Find the vector equation of the plane.
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"`.
Find the Cartesian equations of the line which passes through the point (–2, 4, –5) and parallel to the line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)`.
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)`.
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"`.
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 point A(– 2, 3, 5) and parallel to the vectors `4hat"i" + 3hat"k" and hat"i" + hat"j"`.
Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).
Find the vector equation of the line `x/1 = (y - 1)/2 = (z - 2)/3`
Find the vector equation of the line passing through the point having position vector `4hat i - hat j + 2hat"k"` and parallel to the vector `-2hat i - hat j + hat k`.
Reduce the equation `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8 to normal form
Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)
Find Cartesian equation of the line passing through the point A(2, 1, −3) and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `hat"i" + 2hat"j" - hat"k"`
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"`
Find vector equation of the plane passing through A(−2 ,7 ,5) and parallel to vectors `4hat"i" - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"`
Find the Cartesian and vector equation of the plane which makes intercepts 1, 1, 1 on the coordinate axes
The vector equation of the line passing through `4hati - hatj + 2hatk` and parallel to `-2hati - hatj + hatk` is ______
The cartesian equation of the line `overliner = (hati + hatj + hatk) + lambda(hatj + hatk)` is ______
If line joining points A and B having position vectors `6overlinea - 4overlineb + 4overlinec` and `-4overlinec` respectively, and the line joining the points C and D having position vectors `-overlinea - 2overlineb - 3overlinec` and `overlinea + 2overlineb - 5overlinec` intersect, then their point of intersection is ______
If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ is ______.
Equation of Z-axis is ______
The equation of line equally inclined to co-ordinate axes and passing through (–3, 2, –5) is ______.
The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then ______.
The centres of the circles x2 + y2 = 1, x2 + y2 + 6x – 2y = 1 and x2 + y2 – 12x + 4y = 1 are ______.
Find the Cartesian equation of the plane passing through A(–1, 2, 3), the direction ratios of whose normal are 0, 2, 5.
If the line `(x - 1)/2 = (y + 1)/3 = z/4` lies in the plane 4x + 4y – kz = 0, then the value of k is ______.
Find the direction cosines of the line `(2x - 1)/3 = 3y = (4z + 3)/2`
