Advertisements
Advertisements
प्रश्न
Find `vec"a"*vec"b"` when `vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`
उत्तर
`vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`
`vec"a" * vec"b" = (hat"i" - 2hat"j" + hat"k")*(3hat"i" - 4hat"j" - 2hat"k")`
= (1)(3) + (– 2)(– 4) + (1)(– 2)
= 3 + 8 – 2
= 9
APPEARS IN
संबंधित प्रश्न
If `|vec"a"|= 5, |vec"b"| = 6, |vec"c"| = 7` and `vec"a" + vec"b" + vec"c" = vec"0"`, find `vec"a" * vec"b" + vec"b" *vec"c" + vec"c" * vec"a"`
If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that
`sin theta/2 = 1/2|vec"a" - vec"b"|`
Find `vec"a"*vec"b"` when `vec"a" = 2hat"i" + 2hat"j" - hat"k"` and `vec"b" = 6hat"i" - 3hat"j" + 2hat"k"`
Find the value λ for which the vectors `vec"a"` and `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + 4hat"j" - hat"k"` and `vec"b" = 3hat"i" - 2hat"j" + lambdahat"k"`
Find the angle between the vectors
`hat"i" - hat"j"` and `hat"j" - hat"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"`
Let `vec"a", vec"b", vec"c"` be three vectors such that `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 5` and each one of them being perpendicular to the sum of the other two, find `|vec"a" + vec"b" + vec"c"|`
Find the magnitude of `vec"a" xx vec"b"` if `vec"a" = 2hat"i" + hat"j" + 3hat"k"` and `vec"b" = 3hat"i" + 5hat"j" - 2hat"k"`
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 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"`
If `vec"a", vec"b", vec"c"` are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is `1/2 |vec"a" xx vec"b" + vec"b" xx vec"c" + vec"c" xx vec"a"|`. Also deduce the condition for collinearity of the points A, B, and C
For any vector `vec"a"` prove that `|vec"a" xx hat"i"|^2 + |vec"a" xx hat"j"|^2 + |vec"a" xx hat"k"|^2 = 2|vec"a"|^2`
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 `vec"OP"` makes 60° and 45° with the positive direction of the x and y axes respectively. Then the angle between `vec"OP"` and the z-axis is
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:
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
