Question

For what values of c are the vectors 3i-2j and 2i+3j + ck are perpendicular​

Answer 1

$\textbf{Given:}$

$\textsf{Vectors}\;\mathsf{3\overrightarrow{i}-2\overrightarrow{j}+0\overrightarrow{k}\;\;and\;\;2\overrightarrow{i}+3\overrightarrow{j}+c\overrightarrow{k}\;are\;perpendicular}$

$\textbf{To find:}$

$\textsf{The value of 'c'}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{7cm} \\\textsf{If two vectors are perpendicular, then their}\\\\\textsf{Scalar product is zero} \end{minipage}}$

$\implies\mathsf{(3\overrightarrow{i}-2\overrightarrow{j}+0\overrightarrow{k})\,.\,(2\overrightarrow{i}+3\overrightarrow{j}+c\overrightarrow{k})=0}$

$\implies\mathsf{3(2)+(-2)(3)+0(c)=0}$

$\implies\mathsf{6-6=0}$

$\implies\mathsf{0=0}$

$\textsf{It shows that the scalar product vanishes independent of c}$

$\therefore\textsf{c can take any real value }$

Answer 2

Answer: C can be any number

Step-by-step explanation:  Let A=|3i - 2j| and B=|2i + 3j + ck|

A.B = 0 for two perpendicular vectors

|3i - 2j + 0k|.|2i +3j +ck| = 0

(3i)(2i) + (-2j)(3j) + (0k)(ck) = 0

6 - 6 + 0c = 0

0c = 0

since any number multiplied by zero is zero the value of c can be any number.