Question

Let $\overrightarrow{ a }=2 \hat{i}-7 \hat{j}+5 \hat{k}, \overrightarrow{ b }=\hat{i}+\hat{k}$ and $\overrightarrow{ c }=\hat{i}+2 \hat{j}-3 \hat{k}$ be three given vectors If $\overrightarrow{ r }$ is a vector such that $\vec{r} \times \vec{a}=\vec{c} \times \vec{a}$ and $\vec{r} \cdot \vec{b}=0$, then $|\vec{r}|$ is equal to :

• A. $\frac{11}{7} \sqrt{2}$
• B. $\frac{11}{7}$
• C. $\frac{\sqrt{914}}{7}$
• D. $\frac{11}{5} \sqrt{2}$

Answer 1

Answer: (A)

$\frac{11}{7} \sqrt{2}$

Answer 2

a=2i^−7j^​+5k^
b=i^+k^
c=i^+2j^​−3k^
r×a=c×a⇒(r−c)×a=0
∴r=c+λa
r⋅b=0⇒c⋅b+λb⋅a=0
−2+λ(7)=0⇒λ=72​
∴r=c+72a​=71​(11i^−11k^)
∣r=7112​​