Question

the following vectors is/are perpendicular to 5k

OPTIONS were given in the attached file​

Answer 1

Explanation:

(i) If vector A and B are perpendicular,

then, A.B=0

where, (A= a1i+a2j+a3k) and (B=b1i+b2j+b3k)!

1. Let (A=0i+0j+5k) (B=4i+3j+0k),

A.B= [(0)(4)]i+[(0)(3)]j+[(5)(0)]

A.B.= 0

Their vector product is zero

Hence the are perpendicular.

2. Let (A=0i+0j+5k) (B=6i+0j+0k)

A.B=[(0)(6)]i+[(0)(0)]j+[(5)(0)]k

A.B=0

Hence they are perpendicular.

3. Let (A=0i+0j+5k) (B=0i+0j+7k)

A.B=[(0)(0)]i+[(0)(0)]j+[(5)(7)]

A.B=35

Hence they are not perpendicular.

4. Let (A=0i+0j+5k) (B=3i+4j+0k)

A.B=[(0)(3)]i+[(0)(4)]j+[(5)(0)]k

A.B=0

Hence they are perpendicular.

Hope It Helps!