Advertisement Remove all ads

If aba¯.b¯=3 and abijka¯×b¯=2i^+j^+2k^, find the angle between aa¯ and bb¯. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

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"`.

Advertisement Remove all ads

Solution

Let θ be the angle between `bar"a"` and `bar"b"`

∵ `bar"a" xx bar"b" = 2hat"i" + hat"j" + 2hat"k"`

∴ `|bar"a" xx bar"b"| = sqrt(2^2 + 1^2 + 2^2) = sqrt(4 + 1 + 4) = 3`

∴ `|bar"a"||bar"b"|` sin θ = 3      ...(1)

∴ `bar"a".bar"b" = sqrt3`

∴ `|bar"a"||bar"b"| "cos" theta = sqrt3`     ....(2)

∴ Dividing (1) by (2), we get

`(|bar"a"||bar"b"| "sin" theta)/(|bar"a"||bar"b"| "cos" theta) = 3/sqrt3`

∴ tan θ = `sqrt3 = tan 60^circ`

∴ θ = 60°

Concept: Vector Product of Vectors (Cross)
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×