If ${\bf{\hat u}}\;{\rm{and\;}}{\bf{\hat v}}$ unit vectors and ${\rm{\theta }}$ is the acute angle between them, then $2{\bf{\hat u}} \times 3{\bf{\hat v}}$ is a unit vector for

Exactly one value of ${\rm{\theta }}$

Exactly two values of ${\rm{\theta }}$

More than two values of ${\rm{\theta }}$

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

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Application +4 | -1

\mathbf{\hat u}\;\mathrm{and\;}\mathbf{\hat v}

unit vectors and

\mathrm{\theta }

is the acute angle between them, then

2\mathbf{\hat u} \times 3\mathbf{\hat v}

is a unit vector for

View answer and explanation

Correct option: D

Exactly one value of

\mathrm{\theta }

Option D (Exactly one value of

\mathrm{\theta }

) is correct because the sine function has a unique value between 0 and 90 degrees for a given value between 0 and 1.

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{\hat j}

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\frac{\text { Projection of vector } \mathbf{a} \text { on vector } \mathbf{b}}{\text { Projection of vector } \mathbf{b} \text { on vector } \mathbf{a}}

{\mathbf{\vec a}}

{\mathbf{\vec b}}

\frac{{5\pi }}{6}

{\mathbf{\vec a}}

{\mathbf{\vec b}}

\frac{{ - 6}}{{\sqrt 3 }}

\left| {\mathbf{\vec a}} \right|

\frac{1}{4} \mathrm{~m} / \mathrm{s}

O A

O B

30^{\circ}

45^{\circ}

O B

2x + 4y - 5z = 10