Question

plzzz solve this question

Answer 1

Hello Friend,

Notation in my answer:

• A single capital letter denotes a vector. Eg. : A, B
• i,j,k are the unit vectors along the coordinate axes
• Magnitude of a vector A will be written as |A|
• Dot product of vectors P and Q will be written as P.Q

Now, coming to the solution:

→ A = i + j + k
B = - i - j - k
So, |A| = √(1²+1²+1²) = √3

Now,
A - B = (i+j+k) - (-i-j-k)
So, A - B = 2i + 2j + 2k

Also, |A - B| = √(2²+2²+2²) = 2√3

→ Let angle between (A - B) and A be θ

We can find angle easily with help of dot (scalar) product.

We know that:

P.Q = |P| |Q| cos θ

So, here,

(A - B) . A = |A - B| |A| cos θ
So, (2i + 2j + 2k).(i + j + k) = (2√3) (√3) cosθ
So, (2+2+2) = 6 cos θ
So, 6 = 6 cos θ
So, cos θ = 1
So, θ = 0

This means that the vectors A-B and A are parallel to each other.

→ Thus, the angle between A-B and A is 0

Hope it helps.

Purva
@Purvaparmar1405
Brainly.in