Advertisements
Advertisements
प्रश्न
Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are 1, 3, 2 and –1, 1, 2
उत्तर
Let L1 and L2 be the two lines with direction ratios 1, 3, 2 and –1, 1, 2 respectively.
Let the direction ratios of the vector perpendicular to L1 and L2 be a, b, c.
∴ a + 3b + 2c = 0
and −a + b + 2c = 0
∴ `"a"/|(3, 2),(1, 2)| = (-"b")/|(1, 2),(-1, 2)| = "c"/|(1, 3),(-1, 1)|`
∴ `"a"/(6 - 2) = (-"b")/(2 + 2) = "c"/(1 + 3)`
∴ `"a"/4 = (-"b")/4 = "c"/4`
∴ The direction ratios of the vector are 4, – 4, 4.
APPEARS IN
संबंधित प्रश्न
Find the values of c so that for all real x, the vectors `"xc"hat"i" - 6hat"j" + 3hat"k"` and `"x"hat"i" + 2hat"j" + 2"cx"hat"k"` make an obtuse angle.
Show that the sum of the length of projections of `"p"hat"i" + "q"hat"j" + "r"hat"k"` on the coordinate axes, where p = 2, q = 3 and r = 4 is 9.
Suppose that all sides of a quadrilateral are equal in length and opposite sides are parallel. Use vector methods to show that the diagonals are perpendicular.
If `hat"p", hat"q"` and `hat"r"` are unit vectors `hat"p"+hat "r" = hat "q"`, find `hat"p".hat"q".`
If a line makes angles 90°, 135°, 45° with the X-, Y- and Z-axes respectively, then find its direction cosines.
The direction ratios of `bar"AB"` are −2, 2, 1. If A = (4, 1, 5) and l(AB) = 6 units, find B.
If `bar"a" = 2hat"i" + 3hat"j" - hat"k"`, `bar"b" = hat"i" - 4hat"j" + 2hat"k"`, find `(bar"a" + bar"b") xx (bar"a" - bar"b")`
Find a unit vector perpendicular to the vectors `hat"j" + 2hat"k"` and `hat"i" + hat"j"`.
If `bar"a".bar"b" = sqrt3` and `bar"a" xx bar"b" = 2hat"i" + hat"j" + 2hat"k"`, find the angle between `bar"a"` and `bar"b"`.
If `bar"a" = 2hat"i" + hat"j" - 3hat"k"` and `bar"b" = hat"i" - 2hat"j" + hat"k"`, find a vector of magnitude 5 perpendicular to both `bar"a"` and `bar"b"`.
Find `bar"u".bar"v"` if `|bar"u"| = 2, |bar"v"| = 5, |bar"u" xx bar"v"| = 8`
Find `|bar"u" xx bar"v"|` if `|bar"u"| = 10, |bar"v"| = 2, bar"u".bar"v" = 12`
If `bar"a" = hat"i" - 2hat"j" + 3hat"k"` , `bar"b" = 4hat"i" - 3hat"j" + hat"k"` , `bar"c" = hat"i" - hat"j" + 2hat"k"` verify that `bar"a"xx(bar"b" + bar"c") = bar"a" xx bar"b" + bar"a" xx bar"c"`
Find the area of the parallelogram whose adjacent sides are `bar"a" = 2hat"i" - 2hat"j" + hat"k"` and `bar"b" = hat"i" - 3hat"j" - 3hat"k"`
Find the area of parallelogram whose diagonals are determined by the vectors `bar"a" = 3hat"i" - hat"j" - 2hat"k"` and `bar"b" = - hat"i" + 3hat"j" - 3hat"k"`.
If `bar"a", bar"b", bar"c", bar"d"` are four distinct vectors such that `bar"a" xx bar"b" = bar"c" xx bar"d"` and `bar"a" xx bar"c" = bar"b" xx bar"d"` prove that `bar"a" - bar"d"` is parallel to `bar"b" - bar"c"`.
If `bar"a" = hat"i" + hat"j" + hat"k" "and" bar"c" = hat"j" - hat"k"`, find `bar"a"` vector `bar"b"` satisfying `bar"a" xx bar"b" = bar"c" "and" bar"a".bar"b" = 3`
Find `bar"a"` if `bar"a" xx hat"i" + 2bar"a" - 5hat"j" = bar"0"`
Prove, by vector method, that sin (α + β) = sin α . cos β + cos α . sin β
Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are - 2, 1, - 1 and - 3, - 4, 1
If A(1, 2, 3) and B(4, 5, 6) are two points, then find the foot of the perpendicular from the point B to the line joining the origin and the point A.
The angle θ between two non-zero vectors `bar("a")` and `bar("b")` is given by cos θ = ______
If `|bar("a")*bar("b")| = |bar("a") xx bar("b")|` and `bar("a")*bar("b") < 0`, then find the angle between `bar("a")` and `bar("b")`
If the line r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")` is parallel to the plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 10, then the value of m is ______.
The area of triangle ABC in which c = 8 , b = 3, ∠A = 60° is ______
Let `bar"a" = 2hat"i" + hat"j" - 2hat"k" and bar"b" = hat"i" + hat"j"`. Let `vec"c"` be a vector such that `|bar"c" - bar"a"| = 3, |(bar"a" xx bar"b") xx bar"c"|` = 3 and the angle between `vec"c" and vec"a" xx vec"b" "be" 30^circ`. Then `vec"a" * vec"c"` is equal to ______.
If `overlinea = hati + hatj + hatk` and `overlinec = hatj - hatk` and `overlineb` is a vector satisfying `overlinea xx overlineb = overlinec` and `overlinea . overlineb = 3`, then `3|overlineb|^2` is equal to ______
If `vec"a" = hat"i" + hat"j" + hat"k"` and `vec"c" = hat"j" - hat"k"`. find a vector `vec"b"` satisfying `vec"a" xx vec"b" = vec"c"` and `vec"a"·vec"b"` = 3.
For non zero, non collinear vectors `vecp` and `vecq`, the value of `[(hati, vecp, vecq)]hati + [(hatj, vecp, vecq)]hatj + [(hatk, vecp, vecq)]hatk` is ______.
Find two unit vectors each of which is perpendicular to both `baru and barv, "where" baru = 2hati + hatj - 2hatk , barv = hati + 2hatj - 2hatk`
Find two unit vectors each of which is perpendicular to both `baru "and" barv`, where `baru =2hati + hatj - 2hatk, barv =hati + 2hatj - 2hatk `
Find two unit vectors each of which is perpendicular to both
`baru "and" barv, "where" baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
If a vector has direction angles 45º and 60º find the third direction angle.
Find two unit vectors each of which is perpendicular to both `baru and barv, where baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
Find two unit vectors each of which is perpendicular to both `baru and barv` where `baru = 2hati +hatj -2hatk, barv = hati +2hatj-2hatk`
If a vector has direction angles 45° and 60° find the third direction angle.
Find two unit vectors each of which is perpendicular to both `baru and barv, "where" baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
If a vector has direction angles 45ºand 60º find the third direction angle.
Find two unit vectors each of which is perpendicular to both `baru` and `barv` where `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
Find two unit vectors each of which is perpendicular to both `baru and barv , "where" baru = 2hati + hatj - 2hatk, barv = hati + 2hatj -2hatk`
