WB JEE 2024 | Vector Algebra Question 2 | Physics

1

WB JEE 2024

MCQ (Single Correct Answer)

+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

MCQ (Single Correct Answer)

+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

MCQ (Single Correct Answer)

+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

MCQ (Single Correct Answer)

+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

$${1 \over 2}$$, $${1 \over 2}$$, $${1 \over 2}$$