1
COMEDK 2024 Morning Shift
+1
-0

$$\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=$$

A
3
B
12
C
8
D
16
2
COMEDK 2023 Morning Shift
+1
-0

The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$ is

A
$$\sin ^{-1}(1 / 9)$$
B
$$\sin ^{-1}(8 / 9)$$
C
$$\cos ^{-1}(8 / 9)$$
D
$$\cos ^{-1}(1 / 9)$$
3
COMEDK 2023 Morning Shift
+1
-0

If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$m$$ is

A
$$\frac{5}{8}$$
B
$$\frac{8}{5}$$
C
$$\frac{-7}{4}$$
D
$$\frac{2}{3}$$
4
COMEDK 2023 Morning Shift
+1
-0

$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is

A
$$\frac{1}{3}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$
B
$$\frac{1}{2}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$
C
$$\frac{1}{3}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}})$$
D
None of these
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