Advertisements
Advertisements
प्रश्न
Find the area of the parallelogram whose two adjacent sides are determined by the vectors `hat"i" + 2hat"j" + 3hat"k"` and `3hat"i" - 2hat"j" + hat"k"`
Advertisements
उत्तर
Let the given vectors be `vec"a" = hat"i" + 2hat"j" + 3hat"k"`
`vec"b" = 3hat"i" - 2hat"j" + hat"k"`
`vec"a" xx vec"b" = |(hat"i", hat"j", hat"k"),(1, 2, 3),(3, -2, 1)|`
= `hat"i"(2 + 6) - hat"j"(1 - 9) + hat"k"(-2 - 6)`
= `8hat"i" + 8hat"j" - 8hat"k"`
`|vec"a" xx vec"b"| = sqrt(8^2 + 8^2 + (-8)^2`
= `sqrt(3 xx 8^2)`
= `8sqrt(3)`
The area of the parallelogram with adjacent sides `vec"a"` and `vec"b"`
A = `|vec"a" xx vec"b"|`
= `8sqrt(3)` sq.units
APPEARS IN
संबंधित प्रश्न
If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that
`tan theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`
Find `vec"a"*vec"b"` when `vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`
If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + 2vec"b" + vec"c"` = 0 and `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 7`, find the angle between `vec"a"` and `vec"b"`
Find λ, when the projection of `vec"a" = lambdahat"i" + hat"j" + 4hat"k"` on `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"` is 4 units
Three vectors `vec"a", vec"b"` and `vec"c"` are such that `|vec"a"| = 2, |vec"b"| = 3, |vec"c"| = 4`, and `vec"a" + vec"b" + vec"c" = vec0`. Find `4vec"a"*vec"b" + 3vec"b"*vec"c" + 3vec"c"*vec"a"`
Show that `vec"a" xx (vec"b" + vec"c") + vec"b" xx (vec"c" + vec"a") + vec"c" xx (vec"a" + vec"b") = vec0`
Find the unit vectors perpendicular to each of the vectors `vec"a" + vec"b"` and `vec"a" - vec"b"`, where `vec"a" = hat"i" + hat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"`
Let `vec"a", vec"b", vec"c"` be unit vectors such that `vec"a" * vec"b" = vec"a"*vec"c"` = 0 and the angle between `vec"b"` and `vec"c"` is `pi/3`. Prove that `vec"a" = +- 2/sqrt(3) (vec"b" xx vec"c")`
Find the angle between the vectors `2hat"i" + hat"j" - hat"k"` and `hat"i" + 2hat"j" + hat"k"` using vector product
Choose the correct alternative:
The vectors `vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"` are
Choose the correct alternative:
If `lambdahat"i" + 2lambdahat"j" + 2lambdahat"k"` is a unit vector, then the value of `lambda` is
Choose the correct alternative:
If `|vec"a" + vec"b"| = 60, |vec"a" - vec"b"| = 40` and `|vec"b"| = 46`, then `|vec"a"|` is
Choose the correct alternative:
If `|vec"a"| = 13, |vec"b"| = 5` and `vec"a" * vec"b"` = 60° then `|vec"a" xx vec"b"|` is
Choose the correct alternative:
If the projection of `5hat"i" - hat"j" - 3hat"k"` on the vector `hat"i" + 3hat"j" + lambdahat"k"` is same as the projection of `hat"i" + 3hat"j" + lambdahat"k"` on `5hat"i" - hat"j" - 3hat"k"`, then λ is equal to
Choose the correct alternative:
If (1, 2, 4) and (2, – 3λ – 3) are the initial and terminal points of the vector `hat"i" + 5hat"j" - 7hat"k"` then the value of λ is equal to
Choose the correct alternative:
If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = 2hat"i" + xhat"j" + hat"k", vec"c" = hat"i" - hat"j" + 4hat"k"` and `vec"a" * (vec"b" xx vec"c")` = 70, then x is equal to
