1
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
$$\sqrt{6}$$
2
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
3
KCET 2022
MCQ (Single Correct Answer)
+1
-0

If $$|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$$ and $$|\mathbf{a}|=3$$, then $$|\mathbf{a}|$$ is equal to

A
9
B
36
C
4
D
2
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0

If $$\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$, then express $$\beta$$ in the form $$\beta=\beta_1+\beta_2$$ where $$\beta_1$$ is parallel to $$\alpha$$ and $$\beta_2$$ is perpendicular to $$\alpha$$, then $$\beta_1$$ is given by

A
$$\frac{-1}{2} \hat{\mathbf{i}}+\frac{3}{2} \hat{\mathbf{j}}$$
B
$$\frac{5}{8}(\hat{\mathbf{i}}+3 \hat{\mathbf{j}})$$
C
$$\hat{\mathbf{i}}-3 \hat{\mathbf{j}}$$
D
$$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}$$
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