find the smallest possible length of the vector v

Question

Q1. Let v = $(-2/3,b,16/7)$ and w=$(3/4,-12/5,c)$ be vectors in $R^3$

(a)Find the smallest possible length of vector

My Effort:
v= $(-2/3,b,16/7)$

|a|=$\sqrt{((-2/3)^2+b^2+(16/7)^2)}$

=$\sqrt{(50/21 +b^2)}$

Is this correct for the smallest possible length

Answer 1

HINT

Recall the definition of length, that is $$\vec u=(A,B,C)\implies \|\vec u\|=\sqrt{A^2+B^2+C^2}\ge 0$$

and that

• $f(x) = \sqrt x$ is strictly increasing
• for any $y\in \mathbb{R}$ we have $y^2\ge 0$

Answer 2

Use that $$|\vec{v}|=\sqrt{\left(\frac{-2}{3}\right)^2+b^2+\left(\frac{16}{7}\right)^2}$$