Advertisements
Advertisements
प्रश्न
Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`
उत्तर
The given vectors are `hat"i" + 3hat"j" + 7hat"k"` and `2hat"i" + 6hat"j" + 3hat"k"`
Projection of `hat"i" + 3hat"j" + 7hat"k"` on `2hat"i" + 6hat"j" + 3hat"k"`
= `((hat"i" + 3hat"j" + 7hat"k")*(2hat"i" + 6hat"j" + 3hat"k"))/(|2hat"i" + 6hat"j" + 3hat"k"|)`
= `((1)(2) + (3)(6) + (7)(3))/sqrt(2^2 + 6^2 + 3^2)`
= `(2 + 18 + 21)/sqrt(4 + 36 + 9)`
= `41/sqrt(49)`
= `41/7`
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"`
Find the value λ for which the vectors `vec"a"` and `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" - 2hat"j" + 3hat"k"`
Show that the vectors `-hat"i" - 2hat"j" - 6hat"k", 2hat"i" - hat"j" + hat"k"` and find `-hat"i" + 3hat"j" + 5hat"k"` form a right angled triangle
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"`
Find the vectors of magnitude `10sqrt(3)` that are perpendicular to the plane which contains `hat"i" + 2hat"j" + hat"k"` and `hat"i" + 3hat"j" + 4hat"k"`
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"`
Find the area of the triangle whose vertices are A(3, – 1, 2), B(1, – 1, – 3) and C(4, – 3, 1)
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:
A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to
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"` and `vec"b"` having same magnitude and angle between them is 60° and their scalar product `1/2` is then `|vec"a"|` is
Choose the correct alternative:
Vectors `vec"a"` and `vec"b"` are inclined at an angle θ = 120°. If `vec"a"| = 1, |vec"b"| = 2`, then `[(vec"a" + 3vec"b") xx (3vec"a" - vec"b")]^2` is equal to
Choose the correct alternative:
If `vec"a"` and `vec"b"` are two vectors of magnitude 2 and inclined at an angle 60°, then the angle between `vec"a"` and `vec"a" + vec"b"` is
Choose the correct alternative:
If `vec"a" = hat"i" + 2hat"j" + 2hat"k", |vec"b"|` = 5 and the angle between `vec"a"` and `vec"b"` is `pi/6`, then the area of the triangle formed by these two vectors as two sides, is
