1
KCET 2023
MCQ (Single Correct Answer)
+1
-0

If $$\mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0$$ and $$(\mathbf{a} \times \mathbf{b})+(\mathbf{b} \times \mathbf{c})+(\mathbf{c} \times \mathbf{a})=\lambda(\mathbf{b} \times \mathbf{c})$$, then the value of $$\lambda$$ is equal to

A
3
B
4
C
6
D
2
2
KCET 2023
MCQ (Single Correct Answer)
+1
-0

If $$|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$$, then

A
$$\vec{a}$$ and $$\vec{b}$$ are parallel.
B
$$\vec{a}$$ and $$\vec{b}$$ are coincident.
C
inclined to each other at $$60^{\circ}$$.
D
$$\vec{a}$$ and $$\vec{b}$$ are perpendicular.
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

The component of $$\hat{\mathbf{i}}$$ in the direction of the vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ is

A
6
B
$$6 \sqrt{6}$$
C
$$\frac{\sqrt{6}}{6}$$
D
$$\sqrt{6}$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0

If $$|\mathbf{a}|=2$$ and $$|\mathbf{b}|=3$$ and the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$ is $$120^{\circ}$$, then the length of the vector $$\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|$$ is

A
2
B
3
C
1/6
D
1
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