1
KCET 2019
MCQ (Single Correct Answer)
+1
-0

A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is

A
$$\frac{\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}}{\sqrt{3}}$$
B
$$\frac{\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}}{\sqrt{3}}$$
C
$$\frac{-\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}}{\sqrt{3}}$$
D
$$\frac{-\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}}{\sqrt{3}}$$
2
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$[\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=$$

A
$$2[\mathbf{a}, \mathbf{b}, \mathbf{c}]$$
B
0
C
$$3[\mathbf{a}, \mathbf{b}, \mathbf{c}]$$
D
$$[\mathbf{a}, \mathbf{b}, \mathbf{c}]$$
3
KCET 2018
MCQ (Single Correct Answer)
+1
-0
If $|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144$ and $|\vec{a}|=4$, then the value of $|\vec{b}|$ is
A
1
B
2
C
3
D
4
4
KCET 2018
MCQ (Single Correct Answer)
+1
-0
If $\vec{a}$ and $\vec{b}$ are mutually perpendicular unit vectors, then $(3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})$ is equal to
A
5
B
3
C
6
D
12
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