1
WB JEE 2024
+1
-0.25

Let $$\theta$$ be the angle between two vectors $$\vec{A}$$ and $$\vec{B}$$. If $$\hat{a}_{\perp}$$ is the unit vector perpendicular to $$\vec{A}$$, then the direction of $$\overrightarrow{\mathrm{B}}-\mathrm{B} \sin \theta \hat{\mathrm{a}}_{\perp} \text { is }$$

A
along $$\vec{B}$$
B
perpendicular $$\vec{B}$$
C
along $$\vec{A}$$
D
perpendicular $$\vec{A}$$
2
WB JEE 2020
+1
-0.25
Consider the vectors $$A = \hat i + \hat j - \hat k$$ ,$$B = 2\hat i - \hat j + \hat k$$ and $$C = {1 \over {\sqrt 5 }}\left( {\hat i - 2\hat j + 2\hat k} \right)$$ . What is the value of C. (A$$\times$$ B) ?
A
1
B
0
C
3$${\sqrt 2 }$$
D
18$${\sqrt 5 }$$
3
WB JEE 2018
+1
-0.25
In a triangle ABC, the sides AB and AC are represented by the vectors $$3\widehat i + \widehat j + \widehat k$$ and $$\widehat i + 2\widehat j + \widehat k$$, respectively. Calculate the angle $$\angle ABC$$.
A
$${\cos ^{ - 1}}\sqrt {{5 \over {11}}}$$
B
$${\cos ^{ - 1}}\sqrt {{6 \over {11}}}$$
C
$$\left( {90^\circ - {{\cos }^{ - 1}}\sqrt {{5 \over {11}}} } \right)$$
D
$$\left( {180^\circ - {{\cos }^{ - 1}}\sqrt {{5 \over {11}}} } \right)$$
4
WB JEE 2017
+1
-0.25
Three vectors $$\overrightarrow A$$ = a$$\widehat i$$ + $$\widehat j$$ + $$\widehat k$$; $$\overrightarrow B$$ = $$\widehat i$$ + b$$\widehat j$$ + $$\widehat k$$ and $$\overrightarrow C$$ = $$\widehat i$$ + $$\widehat j$$ + c$$\widehat k$$ are mutually perpendicular ($$\widehat i$$, $$\widehat j$$ and k are unit vectors along X, Y and Z-axes respectively). The respective values of a, b and c are
A
0, 0, 0
B
$$- {1 \over 2}$$, $$- {1 \over 2}$$, $$- {1 \over 2}$$
C
1, $$-$$1, 1
D
$${1 \over 2}$$, $${1 \over 2}$$, $${1 \over 2}$$
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