Question

Prove that following vectors are perpendicular to each other

(i) 𝑨⃗⃗ =(𝒊̂+𝟐𝒋̂+𝟑𝒌̂) and 𝑩⃗⃗ =(𝟐𝒊̂−𝒋̂)

(ii) 𝑪⃗⃗ =(𝟑𝒊̂−𝟐𝒋̂+𝟖𝒌̂) and 𝑫⃗⃗ =(𝟐𝒊̂+𝟐𝒋̂−𝟏/𝟒𝒌̂)

(iii) 𝑬⃗⃗ =(𝟏𝟖𝒊̂+𝟔𝒋̂+𝟔𝒌̂) and 𝑭⃗⃗ =(−𝟐𝒊̂+𝟑𝒋̂+𝟑𝒌̂)

(iv) 𝑮⃗⃗ =(−𝟔𝒊̂+𝟑/𝟒𝒌̂) and 𝑯⃗⃗⃗ =(𝟏/𝟐𝒊̂+𝟐/𝟑𝒋̂+𝟒𝒌̂)

Answer 1

i) False

$$\begin{vmatrix} i & j & k\\ 1 & 2 & 3\\ 2 & -1 & 0 \end{vmatrix}=(3,6,-5)$$

ii) False

$$\begin{vmatrix} i & j & k\\ 3 & -2 & 8\\ 2 & 2 & -0.25 \end{vmatrix}=(-15.5,16.75,10)$$

iii) False

$$\begin{vmatrix} i & j & k\\ 18 &6 &6\\ -2 & 3 & 3 \end{vmatrix}=(0,-66,66)$$

iv) False

$$\begin{vmatrix} i & j & k\\ -6 &0 &0.75\\ 0.5 & \frac{2}{3} & 4 \end{vmatrix}=(-0.5,24.375,-4)$$