Question

If the vectors 2i + λj - K and 4i - 2j + 2k are perpendicular to each other, find λ.

Answer 1

Answer:

λ=3

Step-by-step explanation:

If the vectors 2i + λj - K and 4i - 2j + 2k are perpendicular to each other, than the angle between them is 90°.

We know that angle between two vectors$\vec a,\vec b$

is given by

$cos\:\theta = \frac{\vec a.\vec b}{|\vec a||\vec b|} \\\\cos 90=\frac{\vec a.\vec b}{|\vec a||\vec b|}\\\\\frac{\vec a.\vec b}{|\vec a||\vec b|}=0\\\\\vec a.\vec b=0$
here

$\vec a=2\hat i+\lambda \hat j-\hat k\\\\\vec b=4\hat i-2 \hat j+2\hat k$

2(4)-2(λ)-1(2)=0

8-2λ-2=0

-2λ=-6

λ=3

Is the required value of λ.

Answer 2

Answer:

Step-by-step explanation:

Yu