1
KCET 2021
+1
-0

A vector a makes equal acute angles on the coordinate axis. Then the projection of vector $$\mathbf{b}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ on $$\mathbf{a}$$ is

A
$$\frac{11}{15}$$
B
$$\frac{11}{\sqrt{3}}$$
C
$$\frac{4}{5}$$
D
$$\frac{3}{5 \sqrt{3}}$$
2
KCET 2021
+1
-0

The diagonals of a parallelogram are the vectors $$3 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$. and $$-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-8 \hat{\mathbf{k}}$$. Then the length of the shorter side of parallelogram is

A
$$2 \sqrt{3}$$
B
$$\sqrt{14}$$
C
$$3 \sqrt{5}$$
D
$$4 \sqrt{3}$$
3
KCET 2021
+1
-0

If $$\mathbf{a} \cdot \mathbf{b}=0$$ and $$\mathbf{a}+\mathbf{b}$$ makes an angle $$60^{\circ}$$ with $$a$$, then

A
$$|\mathbf{a}|=2|\mathbf{b}|$$
B
$$2|\mathbf{a}|=|\mathbf{b}|$$
C
$$|\mathbf{a}|=\sqrt{3}|\mathbf{b}|$$
D
$$\sqrt{3}|\mathbf{a}|=|\mathbf{b}|$$
4
KCET 2021
+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
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