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If (2hat(i)+6hat(j)+ 27hat(k))xx(hat(i)+...

If `(2hat(i)+6hat(j)+ 27hat(k))xx(hat(i)+phat(j)+qhat(k))=vec(0)`, then the values of p and q are ?

A

p=6,q=27

B

`p=3, q=(27)/(2)`

C

`p=6,q=(27)/(2)`

D

`p=3, q=27`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( (2\hat{i} + 6\hat{j} + 27\hat{k}) \times (\hat{i} + p\hat{j} + q\hat{k}) = \vec{0} \), we will follow these steps: ### Step 1: Set up the cross product in determinant form The cross product can be expressed in determinant form as follows: \[ \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 6 & 27 \\ 1 & p & q \end{vmatrix} \]
To solve the equation \( (2\hat{i} + 6\hat{j} + 27\hat{k}) \times (\hat{i} + p\hat{j} + q\hat{k}) = \vec{0} \), we will follow these steps: ### Step 1: Set up the cross product in determinant form The cross product can be expressed in determinant form as follows: \[ \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ ...
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