First slide

Introduction to vectors

Question

$Let a, b, c be distinct non-negative numbers. If the vectors$ $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k} and c \hat{i} + c \hat{j} + b \hat{k} lie in a plane, then c is :$

Easy

A

$the A.M. of a and b$
B

$the G.M. of a and b$
C

$the H.M. of a and b$
D

$equal to zero$

Solution

$Vectors in the same plane, hence$ $|\begin{array}{l} a a c \\ 1 0 1 \\ c c b \end{array}| = 0$
$\begin{matrix} - 1 (a b - c^{2}) - 1 (a c - a c) = 0 \\ c^{2} = a b \end{matrix}$

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