Question

Find the value of lambda so that vector a = 2i+lambda j+k and b=4i+2j-2k are perpendicular t each other

Answer 1

Answer:

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Answer 2

Answer:

$\lambda=-3$

Step-by-step explanation:

We are given that two vectors

$\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k}$

$\vec{b}=4\hat{i}+2\hat{j}-2\hat{k}$

We are given that vector a and b are perpendicular to each other.

We have to find the value of $\lambda$

We know that when two vectors are perpendicular then

$a\cdot b=0$

Using the formula

$(2i+\lambda j+k)\cdot (4i+2j-2k)=0$

Because $i\cdot i=j\cdot j=k\cdot k=1,i\cdot j=j\cdot k=k\cdot i=k\cdot j=j\cdot i=i\cdot k=0$

$8+2\lambda-2=0$

$2\lambda+6=0$

$2\lambda=-6$

$\lambda=\frac{-6}{2}=-3$

Hence, $\lambda=-3$