1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
Position vector of P and Q are $\hat{\imath}+3 \hat{\jmath}-7 \hat{k}$ and $5 \hat{\imath}-2 \hat{\jmath}+4 \hat{k}$ respectively. Then the cosine of the angle between $\overrightarrow{P Q}$ and y -axis is
A
$\frac{4}{\sqrt{162}}$
B
$\frac{5}{\sqrt{162}}$
C
$-\frac{5}{\sqrt{162}}$
D
$-\frac{4}{\sqrt{162}}$
2
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
3
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
$\sqrt{10}$
4
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
$-\frac{1}{\sqrt6}$
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