1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the parallelogram for which $\vec{\alpha}$ and $\vec{\beta}$ are adjacent sides is

A
$\sqrt{17}$
B
$\sqrt{14}$
C
$\sqrt{7}$
D
$\sqrt{41}$
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors. Suppose $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$. Then $\vec{a}$ is

A
$\vec{b} \times \vec{c}$
B
$\vec{c} \times \vec{b}$
C
$\vec{b}+\vec{c}$
D
$\pm 2(\vec{b} \times \vec{c})$
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A unit vector in XY-plane making an angle $$45^{\circ}$$ with $$\hat{i}+\hat{j}$$ and an angle $$60^{\circ}$$ with $$3 \hat{i}-4 \hat{j}$$ is

A
$$ \frac{13}{14} \hat{i}+\frac{1}{14} \hat{j} $$
B
$$ \frac{1}{14} \hat{i}+\frac{13}{14} \hat{j} $$
C
$$ \frac{13}{14} \hat{\mathrm{i}}-\frac{1}{14} \hat{\mathrm{j}} $$
D
$$ \frac{1}{14} \hat{i}-\frac{13}{14} \hat{j} $$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\widehat j + \widehat k,\overrightarrow \beta = \widehat j + a\widehat k$$ and $$\overrightarrow \gamma = a\widehat i + \widehat k$$ is maximum, is

A
3
B
$$-$$3
C
$$ - {1 \over {\sqrt 3 }}$$
D
$${1 \over {\sqrt 3 }}$$
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