TS EAMCET · Maths · Vector Algebra
If two vectors \(\vec{a}\) and \(\vec{b}\) which are perpendicular to each other are such that \(|\vec{a}|=8\) and \(|\vec{b}|=3\), then \(|\vec{a}-2 \vec{b}|=\)
- A \(10\)
- B \(2\)
- C \(6\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(10\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & |\vec{a}|=8,|\vec{b}|=3 \\ & \vec{a} \cdot \vec{b}=0 \\ & |\vec{a}-2 \vec{b}|^2=(\vec{a}-2 \vec{b}) \cdot(\vec{a}-2 \vec{b}) \\ & =|\vec{a}|^2+4|\vec{b}|^2-4 \vec{a} \cdot \vec{b} \\ & =64+36=100 \\ & \therefore \quad|\vec{a}-2 \vec{b}|=10 \text {. } \\ &…
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