CBSE 2026 · Region 3 · Set 1 · Q24 · 2 marks
If for two unit vectors $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}},|\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{~b}}|=|2 \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|$, then find the angle between $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$.
Marking-scheme solution
Given that $\displaystyle |\vec{a}|=|\vec{b}|=1$
$\displaystyle |\vec{a}+2\vec{b}|=|2\vec{a}-\vec{b}| \Rightarrow |\vec{a}+2\vec{b}|^{2}=|2\vec{a}-\vec{b}|^{2}$
$\displaystyle \Rightarrow |\vec{a}|^{2}+4|\vec{b}|^{2}+4\vec{a} \cdot \vec{b}=4|\vec{a}|^{2}+|\vec{b}|^{2}-4\vec{a} \cdot \vec{b} \Rightarrow \vec{a} \cdot \vec{b}=0$
$\displaystyle \Rightarrow$ Angle between $\displaystyle \vec{a}$ and $\displaystyle \vec{b}=\dfrac{\pi}{2}$
Vector AlgebraProduct of Two VectorsApplyvery_short_answermedium
More from Vector Algebra
- If a+ b+ c= 0 such that a =3, b =5, c =7, then find the angle between a and b. OR If a and b are unit vectors…2025 · asked 3×
- The position vectors of points P and Q are p and q respectively. The point R divides line segment PQ in the…2024 · asked 3×
- If a+ b= i and a=2 i-2 j+2 k, then b equals:2023 · asked 3×
- A vector a makes equal angles with all the three axes. If the magnitude of the vector is 5 √3 units, then…2025 · asked 3×
- The vector with terminal point A(2,-3,5) and initial point B(3,-4,7) is:2024 · asked 3×
- Find the position vector of point C which divides the line segment joining points A and B having position…2024 · asked 3×
- If a =2 and -3 ≤ k ≤ 2, then k a ∈:2024 · asked 3×
- Unit vector along PQ, where coordinates of P and Q respectively are (2,1,-1) and (4,4,-7), is2023 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.