If vector a = xi + 2j - zk and vector b = 3i - yj + k. are two equal vectors, then write the value of x + y + z.

Question

If  \(\vec a=\text x\hat i+2\hat j-z\hat k\)  and  \(\vec b=3\hat i-y\hat j+\hat k\), are two equal vectors, then write the value of x + y + z.

Answer 1

Two vectors  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) and  \(\vec b=b_1\hat i+b_2\hat j+b_3\hat k\) are equal, if and only if, a₁ = b_1, a₂ = b₂, a₃ = b₃

Hence, we get x = 3, -y = 2 ⇒ y = -2 and -z = 1 ⇒  z = -1