Question

Find the angul between two vectors A= 2 hat j + hat j - hat k and B=hat j - hat k and B = hati - hatk .

Answer 1

Given:

( a)  A= 2 hat j + hat j - hat k and B=hat j - hat k

( b ) A =  2 hat j + hat j - hat k and B = hati - hatk

To Find:

The angle between the vectors A and B.

Solution:

To find the angle between the vector A and B, we can use the dot product.

We know,

• A.B = |A||B|cos x
• Where x is the angle between the two vectors.

(a) A = 2i + j - k and B = j - k

• A.B = ( 2i + j - k).(j - k) = 0 + 1 + 1 = 2
• |A| = √2² + 1² + -1² = √6
• |B| = √1 + 1 = √2
• if x is the angle between A and B,
• then 2  = √6√2cos x
• cos x = 1/√3
• x = $cos^{- 1}$(1/√3)

(b) A = 2i + j - k and B = i - k

• A.B = ( 2i + j - k).(i - k) = 2 + 0+ 1 = 3

• |A| = √2² + 1² + -1² = √6
• |B| = √1 + 1 = √2
• if x is the angle between A and B,
• then 3  = √6√2cos x
• cos x = √3/2
• x = $cos^{- 1}$(√3/2) = 30 degree