Answer to Question #166200 in Physics for gibson mkandawire

Question #166200

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)


1
Expert's answer
2021-03-09T10:50:18-0500

i) False


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

ii) False


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

iii) False


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

iv) False


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


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