WB JEE 2008 | Vector Algebra Question 1 | Physics

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The angle subtended by the vector $$A = 4\widehat i + 3\widehat j + 12\widehat k$$ with the x-axis is

$${\sin ^{ - 1}}\left( {{3 \over {13}}} \right)$$

$${\sin ^{ - 1}}\left( {{4 \over {13}}} \right)$$

$${\cos ^{ - 1}}\left( {{4 \over {13}}} \right)$$

$${\cos ^{ - 1}}\left( {{3 \over {13}}} \right)$$

WB JEE 2020

MCQ (Single Correct Answer)

-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) ?

3$${\sqrt 2 }$$

18$${\sqrt 5 }$$

WB JEE 2018

MCQ (Single Correct Answer)

-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 $$\angle ABC$$.

$${\cos ^{ - 1}}\sqrt {{5 \over {11}}} $$

$${\cos ^{ - 1}}\sqrt {{6 \over {11}}} $$

$$\left( {90^\circ - {{\cos }^{ - 1}}\sqrt {{5 \over {11}}} } \right)$$

$$\left( {180^\circ - {{\cos }^{ - 1}}\sqrt {{5 \over {11}}} } \right)$$

WB JEE 2017

MCQ (Single Correct Answer)

-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

0, 0, 0

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

1, $$-$$1, 1

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

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