Vector A̅ = ŷ.3 + ẑ.2 and B̅ = x̂.5 + ŷ.8 extend from the origin. Find A̅.B̅ Choose the correct answer.

Question

Question

This question was previously asked in

UGC NET Paper 2: Electronic Science 3rd Dec 2021 Shift 2

Answer 1

Solution:

Dot Product:

The geometric definition of the dot product says that the dot product between two vectors a and b is a⋅b = |a| |b|cosθ

The standard unit vectors are orthogonal (cosθ = 90°), so we conclude that the dot product between a pair of distinct standard unit vectors is zero:
∴ i⋅j = i⋅k = j⋅k = 0
The dot product between a unit vector and itself is also simple to compute. In this case, the angle is zero, and cosθ =1. Given that the vectors are all of length one, the dot products are
∴ i⋅i = j⋅j = k⋅k = 1

Calculation:

A̅ = ŷ.3 + ẑ.2 , B̅ = x̂.5 + ŷ.8

A̅.B̅=3×8=24