Question

The value of lemda for which the two vector A = 5i + lemda j + k and b = i - 2j + k are perpendicular to each other is​

Answer 1

Answer:

answer is 3

dot product concept

Answer 2

Answer:

The value of k is $3$

Explanation:

Given: Two vectors

To find: Value of k

Solution:

For two vectors$\vec{a}$and $\vec{b}$ to be perpendicular, $\vec{a} \cdot \vec{b}=0 .$

Thus,  $(5 \hat{i}+\lambda \hat{j}+\hat{k}) \cdot(\hat{i}-2 \hat{j}+\hat{k})$

$\begin{aligned}&=5(\hat{i} . \hat{i})-2 \lambda(\hat{j} \cdot \hat{j})+1(\hat{k} \cdot \hat{k}) \\&0=5-2 \lambda+1 \\&\Rightarrow 0=6-2 \lambda \Rightarrow \lambda=3\end{aligned}$

Hence the value of k is $3$