Question

For what values of q are the two vectors A = i + j + kq each other and B-iq-23 + 2kg perpendicular to

Answer 1

The value of q are 0.781,-1.281.

Explanation:

Given : Two vectors
`A=i+j+kq` and
`B=iq-2j+2kq` are perpendicular to each other.

To find : The value of q ?

Solution :

When two vectors are perpendicular to each other then their dot product is zero.

i.e.
`\vec{A}\cdot \vec{B}=0`

Two vectors
`A=i+j+kq` and
`B=iq-2j+2kq`

`(i+j+kq)\cdot (iq-2j+2kq)=0`

`(1)(q)+(1)(-2)+(q)(2q)=0`

`q-2+2q^2=0`

`2q^2+q-2=0`

`2q^2+q-2=0`

Using quadratic formula,

`q=(-1\pm√(1^2-4(2)(-2)))/(2(2))`

`q=(-1\pm√(17))/(4)`

`q=(-1+√(17))/(4),(-1-√(17))/(4)`

`q=0.781,-1.281`

Therefore, The value of q are 0.781,-1.281.