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if i,j,k is an orthonormal system of vectors, a is a vector and a cross i +2a-5j=0 then a=

if i,j,k is an orthonormal system of vectors, a is a vector and a cross i +2a-5j=0 then a=

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
6 years ago
let a = xi + yj + zk
then the equation
a \times \hat{i} + 2a - 5\hat{j} = -y\hat{k} + z\hat{j} + 2x\hat{i} + 2y\hat{j} + 2z\hat{k} - 5\hat{j} = 0
2x\hat{i} + (2y + z - 5)\hat{j} + (2z - y)\hat{k} = 0

this implies
x = 0, y = 2z
thus
5z – 5 = 0 => z = 1 and y = 2
thus
a = 2\hat{j} + \hat{k}

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