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mihalych1998 [28]
2 years ago
5

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

Mathematics
1 answer:
Sloan [31]2 years ago
6 0

Answer:

The value of q are 0.781,-1.281.

Step-by-step 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=\frac{-1\pm\sqrt{1^2-4(2)(-2)}}{2(2)}

q=\frac{-1\pm\sqrt{17}}{4}

q=\frac{-1+\sqrt{17}}{4},\frac{-1-\sqrt{17}}{4}

q=0.781,-1.281

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

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