1
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
$$\sqrt{21}, \quad \sqrt{13}$$
2
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
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$ is

A
$$\sin ^{-1}(1 / 9)$$
B
$$\sin ^{-1}(8 / 9)$$
C
$$\cos ^{-1}(8 / 9)$$
D
$$\cos ^{-1}(1 / 9)$$
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$m$$ is

A
$$\frac{5}{8}$$
B
$$\frac{8}{5}$$
C
$$\frac{-7}{4}$$
D
$$\frac{2}{3}$$
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