If `veca and vecb` are two unit vectors perpenicualar to each other and `vecc= lambda_(1)veca+ lambda_2 vecb+ lambda_(3)(vecaxx vecb),` then which of the following is (are) true ?

Options

A. `lambda_(1)= veca.vecc`
B. `lambda_(2)= |vecb xx vecc|`
C. `lambda_(3)= |(vecaxx vecb|xxvecc|`
D. `vecc =lambda_(1)veca + lambda_(2) vecb + lambda_(3) (vecaxxvecb)`

Answer

a,d

Explanation

Given `vecc= lambda_(1)veca+lambda_(2)vecb + lambda_(3)(vecaxxvecb)`
`and veca. vecc= lambda_(1),vecc.vecb=lambda_(2)`
` and vecc. (veca xx vecb) |veca xx vecb|^(2) lambda_(3)`
` (1.1 sin 90^(@))^(2) lambda_(3) = lambda_(3)`
Hence, ` lambda_(1), + lambda_(2), + lambda_(3) = (veca + vecb + veca xx vecb) . vecc`