1
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If $$\theta$$ be the angle between the vectors $$a = 2\widehat i + 2\widehat j - \widehat k$$ and $$b = 6\widehat i - 3\widehat j + 2\widehat k$$, then

A
$$\cos \theta = {4 \over {21}}$$
B
$$\cos \theta = {3 \over {19}}$$
C
$$\cos \theta = {2 \over {19}}$$
D
$$\cos \theta = {5 \over {21}}$$
2
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If x, y and z are non-zero real numbers and $$a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k$$ and $$c = x\widehat i + y\widehat j + z\widehat k$$ are such that $$a \times b = z\widehat i - 3\widehat j + \widehat k$$, then [a b c] is equal to

A
3
B
10
C
9
D
6
3
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

Maximum value of $$z=12x+3y$$, subject to constraints $$x\ge0,y\ge0,x+y\ge5$$ and $$3x+y\le9$$ is

A
15
B
36
C
60
D
40
4
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If $$\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$$ and $$\mathbf{r}=\hat{i}+\hat{k}$$, then the unit vector in the direction of $$3 p+q-2 r$$ is

A
$$\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})$$
B
$$\frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k})$$
C
$$\frac{1}{3}(\hat{i}-2 \hat{j}+2 \hat{k})$$
D
$$\hat{i}+2 \hat{j}+2 \hat{k}$$
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