Question

91. A vector perpendicular to (4i+3j)
may be
(1) 4i +3j
(2) 7k
(3) 6i
(4) 3î +4j
pleased explain with procedure​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• A vector 4î + 3j.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Find:- }}}}$

• The vector perpendicular to the given vector .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution:- }}}}$

We know that if two vectors are perpendicular , then their dot product is zero . As the dot product of two vectors A and B is given by |A| |B| cos θ , so that when θ is 90° , therefore the dot product will be 0 .

• Let the vector perpendicular to that vector be xî + yj . So that ,

$\sf\dashrightarrow ( 4\hat{i} + 3\hat{j}).( x\hat{i}+y\hat{i} ) = 0 \\\\\\\sf\dashrightarrow 4x + 3y = 0 \\\\\\\sf\dashrightarrow 4x = -3y \\\\\\\sf\dashrightarrow \pink{ x/y = -3/4 }$

Therefore the vector perpendicular to the given vector will be ,

$\sf\dashrightarrow \boxed{\pink{\sf Vector = -3\hat{i} + 4\hat{j} }}$