KCET 2026 | Vector Algebra Question 1 | Mathematics

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

$\dfrac{5}{2}$

$\dfrac{-5}{2}$

$\dfrac{2}{5}$

$\dfrac{-2}{5}$

KCET 2026

MCQ (Single Correct Answer)

-0

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

$\dfrac{5}{3}\hat{i} - \dfrac{2}{3}\hat{j} + \dfrac{2}{3}\hat{k}$

$\dfrac{5}{3}\hat{i} + \dfrac{2}{3}\hat{j} - \dfrac{2}{3}\hat{k}$

$\dfrac{5}{3}\hat{i} + \dfrac{2}{3}\hat{j} + \dfrac{2}{3}\hat{k}$

$-\dfrac{5}{3}\hat{i} + \dfrac{2}{3}\hat{j} + \dfrac{2}{3}\hat{k}$

KCET 2026

MCQ (Single Correct Answer)

-0

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to

$2$

$-1$

$0$

$1$

KCET 2025

MCQ (Single Correct Answer)

-0

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

$\pm 1$

-1

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