1.

If a=(1)/(sqrt(10))(3hati+hatk) and b=(1)/(7)(2hati+3hatj-6hatk), then the value of (2a-b).[(axxb)xx(a+2b)] is

Answer»

`-3`
5
3
`-5`

Solution :GIVEN , `a = 1/(SQRT(10)) (hati + hatk)`and `b = 1/(7) (2hati + 3hatj - 6hatk)`
`:. (2a-b) .[(a xx b) xx (a+2B)]`
`= (2a - b).{(a xx b)xx a + (a xx b) xx 2b }`
`= (2a - b) .{(a.a) b - (b.a) a+ 2 (a.b) b - 2(b.b)a}`
`= (2a - b) .{1(b)- (0) a + 2(0) b - 2 (1)a}`
[ `:' a .b = 0` and ` a.a = b = 1`]
`= (2a - b) (b - 2a) = - (4|a|^(2) - 4A. b + |b|^(2))`
`= - {4 - 0 + 1} = - 5`


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