Question

For what value of a of two vectors 2i+3j+ak and 1+2aj-k are perpendicular each other

Answer 1

If two vectors 2i+3j+ak and 1i+2aj-k are perpendicular each other then the value of a is [-2/5].

Step-by-step explanation:

Let’s assume vector (2i + 3j + ak) be denoted as vector “P” and vector (1i + 2aj – k) be denoted as vector “Q”.

We are given that the two vectors are perpendicular to each other which means the angle between them θ = 90° and cos 90°= 0.  

Therefore, the dot product of the two vectors P & Q will be 0 i.e.,

P.Q = 0

⇒ (2i + 3j + ak) . (1i + 2aj – k) = 0

⇒ 2 + 6a – a = 0

⇒ 2 + 5a = 0

⇒ 5a = - 2

⇒ a = -$\frac{2}{5}$

Thus, the value of a is -$\frac{2}{5}$ .

---------------------------------------------------------------------------

Also View:

The resultant of two vectors P and Q is perpendicular to P and its magnitude is half of that of Q. Whats the angle between P and Q?

https://brainly.in/question/5084939

If x and y components of a vector vector P have numerical values 3 and 4 respectively and that affected p p + vector Q have numerical values 8 and 7 respectively then the magnitude of vector Q is

https://brainly.in/question/13484638