1
KCET 2021
MCQ (Single Correct Answer)
+1
-0

If the area of the parallelogram with $$\mathbf{a}$$ and $$\mathbf{b}$$ as two adjacent sides is 15 sq units, then the area of the parallelogram having $$\mathrm{3 a+2 b}$$ and $$\mathbf{a}+3 \mathbf{b}$$ as two adjacent sides in sq units is

A
45
B
75
C
105
D
120
2
KCET 2020
MCQ (Single Correct Answer)
+1
-0

The two vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$$ represent the two sides $$\overline{A B}$$ and $$\overline{A C}$$ respectively of a $$\triangle A B C$$. The length of the median through $$A$$ is

A
$$\frac{\sqrt{14}}{2}$$
B
14
C
7
D
$$\sqrt{14}$$
3
KCET 2020
MCQ (Single Correct Answer)
+1
-0

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are unit vectors and $$\theta$$ is the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$, then $$\sin \frac{\theta}{2}$$ is equal to

A
$$|\mathbf{a}+\mathbf{b}|$$
B
$$\frac{|\mathbf{a}+\mathbf{b}|}{2}$$
C
$$\frac{|\mathbf{a}-\mathbf{b}|}{2}$$
D
$$|\mathbf{a}-\mathbf{b}|$$
4
KCET 2020
MCQ (Single Correct Answer)
+1
-0

If $$|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6$$, then $$|\mathbf{b}|$$ is equal to

A
6
B
3
C
2
D
4
KCET Subjects
EXAM MAP