1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Let $$\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}$$ and $$\vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}$$ be two vectors, such that $$\vec{a} \times \vec{b}=-\hat{i}+9 \hat{j}+12 \hat{k}$$. Then the projection of $$\vec{b}-2 \vec{a}$$ on $$\vec{b}+\vec{a}$$ is equal to :

A
2
B
$$\frac{39}{5}$$
C
9
D
$$\frac{46}{5}$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

$$\text { Let } \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k} \text { and } \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat{k} \text {. If }((\vec{a} \times \vec{b}) \times \hat{i}) \cdot \hat{k}=\frac{23}{2} \text {, then }|\vec{b} \times 2 \hat{j}|$$ is equal to :

A
4
B
5
C
$$\sqrt{21}$$
D
$$\sqrt{17}$$
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

Let $$\overrightarrow{\mathrm{a}}=\alpha \hat{i}+\hat{j}-\hat{k}$$ and $$\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$$. If the projection of $$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$$ on the vector $$-\hat{i}+2 \hat{j}-2 \hat{k}$$ is 30, then $$\alpha$$ is equal to :

A
$$\frac{15}{2}$$
B
8
C
$$\frac{13}{2}$$
D
7
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

Let $$\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$$ and let $$\vec{b}$$ be a vector such that $$\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$$ and $$\vec{a} \cdot \vec{b}=3$$. Then the projection of $$\vec{b}$$ on the vector $$\vec{a}-\vec{b}$$ is :

A
$$\frac{2}{\sqrt{21}}$$
B
$$2 \sqrt{\frac{3}{7}}$$
C
$$\frac{2}{3} \sqrt{\frac{7}{3}}$$
D
$$\frac{2}{3}$$
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