Question:medium
For three unit vectors \( \vec a, \vec b, \vec c \) satisfying
\[
|\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9
\]
and
\[
|2\vec a + k\vec b + k\vec c| = 3,
\]
the positive value of \( k \) is:
For three unit vectors \( \vec a, \vec b, \vec c \) satisfying
\[
|\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9
\]
and
\[
|2\vec a + k\vec b + k\vec c| = 3,
\]
the positive value of \( k \) is:
Show Hint
In symmetric vector problems, assuming equal pairwise dot products often simplifies calculations and leads quickly to the correct option.
Updated On: Mar 25, 2026
- \(3\)
- \(6\)
- \(4\)
- \(5\)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Vector Algebra
- The value of \( \hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{j} \times \hat{i}) \) is _____
- GUJCET - 2026
- Mathematics
- Vector Algebra
- If two vectors \( \vec{a} \) and \( \vec{b} \) are such that \( |\vec{a}| = 2, |\vec{b}| = 3 \) and \( \vec{a} \cdot \vec{b} = 4 \), then \( |\vec{a} - \vec{b}| = \)_____
- GUJCET - 2026
- Mathematics
- Vector Algebra
- Let \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \lambda \hat{j} + 2\hat{k} \), where \( \lambda \in \mathbb{Z} \), be two vectors. Let \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} \) be a vector of magnitude \(2\) in the \(yz\)-plane. If \( |\vec{c}| = \sqrt{53} \), then the maximum possible value of \( (\vec{c}\cdot\vec{d})^2 \) is equal to
- JEE Main - 2026
- Mathematics
- Vector Algebra
- Let \( \overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k} \) and \( \overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat{k} \), \( \lambda \in \mathbb{R} \). Let the projection of the vector \( \vec{v} = \hat{i} + \hat{j} + \hat{k} \) on the diagonal \( \overrightarrow{AC} \) of the parallelogram \( ABCD \) be of length one unit. If \( \alpha, \beta \), where \( \alpha>\beta \), be the roots of the equation \( \lambda^2 x^2 - 6\lambda x + 5 = 0 \), then \( 2\alpha - \beta \) is equal to
- JEE Main - 2026
- Mathematics
- Vector Algebra
- Want to practice more? Try solving extra ecology questions todayView All Questions
