Question

Find values of x, y, z if vectors \(\vec{a}\)=x\(\hat{i}\) + 2\(\hat{j}\) + z\(\hat{k}\) and \(\vec{b}\)=2\(\hat{i}\) + y\(\hat{j}\) + \(\hat{k}\) are equal.

(a) x=2, y=2, z=1

(b) x=1, y=2, z=1

(c) x=2, y=1, z=1

(d) x=2, y=2, z=2

This question was posed to me in an interview.

Asked question is from Multiplication of a Vector by a Scalar in section Vector Algebra of Mathematics – Class 12

Answer 1

The correct answer is (a) x=2, y=2, z=1

For explanation I would say: As both the vectors are equal hence, we can equate their constants and get the value of x, y and z. Now we equate the coefficients of \(\hat{i}\), \(\hat{j}\), \(\hat{k}\) of both the equations and get the values x=2, y=2, z=1.