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The angle between the two Vectors vec(A)...

The angle between the two Vectors `vec(A)= 3hat(i)+4hat(j)+5hat(k)` and `vec(B)= 3hat(i)+4hat(j)-5hat(k)` will be

A

Zero

B

`45^(@)`

C

`90^(@)`

D

`180^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(A)= 3hat(i)+4hat(j)+5hat(k), vec(B)= 3hat(i)+4hat(j)-5hat(k)`
`vec(A).vec(B)= (3hat(i)+4hat(j)+5hat(k)).(3hat(i)+4hat(j)-5hat(k))`
`|vec(A)||vec(B)| cos theta = 9+16-25=0`
`|vec(A)|!=0,|vec(B)|!=0, hence, cos theta=0, theta= 90^(@)`
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Knowledge Check

  • The angle between the two vectors, (vec(A)=3hat(i)+4hatj+5hat(k)) and (vec(B)=3hat(i)+4hat(j)-5hat(k)) will be

    A
    zero
    B
    `45^(@)`
    C
    `90^(@)`
    D
    `180^(@)`

  • The angle between two vectors vec(A)= 3hat(i)+4hat(j)+5hat(k) and vec(B)= 3hat(i)+4hat(j)+5hat(k) is

    A
    `60^(@)`
    B
    Zero
    C
    `90^(@)`
    D
    None of these

  • Find th esine of angles between vectors vec(a)= 2hat(i) - 6hat(j) - 3hat(k), and vec(b) = 4hat(i) + 3hat(j)- hat(k) ?

    A
    `(1)/(sqrt26)`
    B
    `(5)/(sqrt26)`
    C
    `(5)/(26)`
    D
    `(1)/(26)`