IIT-JEE 1998 | Vector Algebra and 3D Geometry Question 109 | Mathematics

IIT-JEE 1998

MCQ (More than One Correct Answer)

-0.5

Which of the following expressions are meaningful?

$$u\left( {v \times w} \right)$$

$$\left( {u \bullet v} \right) \bullet w$$

$$\left( {u \bullet v} \right)w$$

$$\,u\, \times \left( {v \bullet w} \right)$$

IIT-JEE 1994

MCQ (More than One Correct Answer)

-1

The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is

a unit vector

makes an angle $${\pi \over 3}$$ with the vector $$\left( {2\widehat i - 4\widehat j + 3\widehat k} \right)$$

parallel to the vector $$\left( { - \widehat i + \widehat j - {1 \over 2}\widehat k} \right)$$

perpendicular to the vector $${3\widehat i + 2\widehat j - 2\widehat k}$$

IIT-JEE 1993

MCQ (More than One Correct Answer)

-0.5

Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k$$ be three vectors. A vector in the plane of $${\overrightarrow b }$$ and $${\overrightarrow c }$$, whose projection on $${\overrightarrow a }$$ is of magnitude $$\sqrt {2/3,} $$ is :

$$2\widehat i + 3\widehat j - 3\widehat k$$

$$2\widehat i + 3\widehat j + 3\widehat k$$

$$-2\widehat i - \widehat j + 5\widehat k$$

$$2\widehat i + \widehat j + 5\widehat k$$

JEE Advanced Subjects