1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $a \neq 0$ and $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c}),|\vec{a}|=|\vec{c}|=1,|\vec{b}|=4$ and $|\vec{b} \times \vec{c}|=\sqrt{15}$ if $\vec{b}-2 \vec{c}=\lambda \vec{a}$ then $\lambda^2$ equals :
A
$-$4
B
16
C
1
D
4
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A line $L_1$ passing through the point A with position vector $\vec{a}=4 \hat{i}+2 \hat{j}+2 \hat{k}$ is parallel to the vector $\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$. The length of the perpendicular drawn from a point P with position vector $\vec{p}=\hat{i}+2 \hat{j}+3 \hat{k}$ to $L_1$ is
A
0
B
$\sqrt{15}$
C
$2\sqrt3$
D
$\sqrt{10}$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The magnitude of the projection of the vector $-\hat{\imath}+2 \hat{\jmath}-\hat{k}$ on the z -axis is
A
2
B
$\frac{1}{\sqrt6}$
C
1
D
$-\frac{1}{\sqrt6}$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are } $$

A
$$\sqrt{3}, \quad \sqrt{14}$$
B
$$\sqrt{13}, \sqrt{14}$$
C
$$\sqrt{21}, \quad \sqrt{3}$$
D
$$\sqrt{21}, \quad \sqrt{13}$$
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