1
COMEDK 2024 Evening Shift
+1
-0

Find the value of '$$b$$' such that the scalar product of the vector $$\hat{\imath}+\hat{\jmath}+\hat{k}$$ with the unit vector parallel to the sum of the vectors $$2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}$$ and $$b \hat{\imath}+2 \hat{\jmath}+3 \hat{k}$$ is unity

A
$$-2$$
B
0
C
$$-1$$
D
1
2
COMEDK 2024 Morning Shift
+1
-0

The vector $$(\vec{r})$$ whose magnitude is $$3 \sqrt{2}$$ units which makes an angle of $$\frac{\pi}{4}$$ and $$\frac{\pi}{2}$$ with $$y$$ and $$z$$- axis respectively is

A
$$\hat{\imath} \pm 3 \hat{\jmath}$$
B
$$\hat{\imath} \pm \hat{\jmath}$$
C
$$-\hat{\imath} \pm \hat{\jmath}$$
D
$$\pm 3 \hat{\imath}+3 \hat{\jmath}$$
3
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
4
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
$$\cos ^{-1}(1 / 9)$$
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