Advertisements
Advertisements
प्रश्न
Prove that `2(bar"a" - bar"b") xx 2(bar"a" + bar"b") = 8(bar"a" xx bar"b")`
उत्तर
LHS = `2(bar"a" - bar"b") xx 2(bar"a" + bar"b")`
`= 4[(bar"a" - bar"b")xx(bar"a" + bar"b")]`
`= 4[bar"a" xx (bar"a" + bar"b") - bar"b" xx (bar"a" + bar"b")]`
`= 4 [bar"a" xx bar"a" + bar"a" xx bar"b" - bar"b" xx bar"a" - bar"b" xx bar"b"]`
= `4[bar0 + bar"a" xx bar"b" + bar"a" xx bar"b" - bar0]` ....`[∵ bar"a" xx bar"a" = bar"b" xx bar"b" = bar"0" "and" - (bar"b" - bar"a") = bar"a" xx bar"b"]`
= `4[2(bar"a" xx bar"b")]`
`= 8 (bar"a" xx bar"b")`
= RHS
∴ `2(bar"a" - bar"b")xx2(bar"a" + bar"b") = 8(bar"a" xx bar"b")`
APPEARS IN
संबंधित प्रश्न
Find two unit vectors each of which is perpendicular to both `baru` and `barv` where `baru = 2hati + hatj - 2hatk`, `barv = hati + 2hatj - 2hatk`.
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.
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.
Find a unit vector perpendicular to the vectors `hat"j" + 2hat"k"` and `hat"i" + hat"j"`.
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`
Show that vector area of a parallelogram ABCD is `1/2 (bar"AC" xx bar"BD")` where AC and BD are its diagonals.
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"`.
Find `bar"a"` if `bar"a" xx hat"i" + 2bar"a" - 5hat"j" = bar"0"`
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"`.
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 value of `hat"i"*(hat"j" xx hat"k") + hat"j"*(hat"i" xx hat"k") + hat"k"*(hat"i" xx hat"j")`.
Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are 1, 3, 2 and –1, 1, 2
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 ______.
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 the vectors `ahat("i")+hat("j")+hat("k"), hat("i")+bhat("j")+hat("k")` and `hat("i")+hat("j")+chat("k")` are coplanar (a ≠ b ≠ c ≠ 1), then the value of abc - (a + b + c) = ______.
If `bar"a"` makes an acute angle with `bar"b", bar"r"*bar"a"` = 0 and `bar"r"xx bar"b" = bar"c" xx bar"b"`, then `bar"r"` = ______.
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.
If `veca, vecb, vecc` are vectors such that `[(veca, vecb, vecc)]` = 4, then `[(veca xx vecb, vecb xx vecc, vecc xx veca)]` = ______.
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`
Find the direction ratios of a line perpendicular to both the lines whose direction ratios are 3, –2, 1 and 2, 4, –2
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`
Find two unit vectors each of which is perpendicular to both `baru and barv,` where `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
