1
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
$\sqrt{10}$
2
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
$-\frac{1}{\sqrt6}$
3
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
$$\sqrt{21}, \quad \sqrt{13}$$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

Find the value of '$$b$$' such that the scalar product of the vector $$\hat{\imath}+\hat{\jmath}+\hat{k}$$ with the unit vector parallel to the sum of the vectors $$2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}$$ and $$b \hat{\imath}+2 \hat{\jmath}+3 \hat{k}$$ is unity

A
$$-2$$
B
0
C
$$-1$$
D
1
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