Question

If,
a = 2î +3j -k
b = i +2j-5k
c = 3i+5j-k
then a vector perpendicular
to
â and
lies
on plane containing
b and c is
​

Answer 1

Answer:

-17i -21j -97k

Step-by-step explanation:

Given vectors are:

a =2i+3j-k

b =i+2j-5k

c =3i+5j-k

Since required vector is in the plane containing vectors b and c therefore

b + λc = 0

(i+2j-5k) + λ(3i+5j-k) = 0

(1+3λ)i + (2+5λ)j - (5+λ)k =0 ......(1)

Direction ratios of vector are:

(1+3λ) , (2+5λ) , -(5+λ)

According to the formula of angle between two lines, if the two vectors are perpendicular (refer to class 12 maths ncert page 472)

(2)(1+3λ) + (3)(2+5λ) + (-1)(-5-λ) = 0

Solving for λ,

λ= -13/22

Putting the value of λ in equation (1)

Required vector is:

-17i -21j -97k