A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 22 - Vector Algebra and 3D Geometry>EXERCISE>Q 16

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The vector $\vec{c}$ directed along the internal bisector of the angle between the vectors $a = 7 \hat{i} - 4 \hat{j} - 4 \hat{k}$ and $b = - 2 \hat{i} - \hat{j} + 2 \hat{k}$ with $| \vec{c} | = 5 \sqrt{6}$ is

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Important Questions on Vector Algebra and 3D Geometry

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 22 - Vector Algebra and 3D Geometry>EXERCISE>Q 17

For three non-zero vectors

\vec{a}, \vec{b}

and

\vec{c}, |(\vec{a} \times \vec{b}) \cdot \vec{c}| = |\vec{a}| |\vec{b}| |\vec{c}|

holds if and only if

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 22 - Vector Algebra and 3D Geometry>EXERCISE>Q 18

If

\hat{a}

and

\hat{b}

are unit vectors, then the greatest value of

|\hat{a} + \hat{b}| + |\hat{a} - \hat{b}|

is

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 22 - Vector Algebra and 3D Geometry>EXERCISE>Q 19

Let the unit vectors

\hat{a}

and

\hat{b}

be perpendicular to each other and the unit vector

\hat{c}

be inclined at an angle

θ

to both

\hat{a}

and

\hat{b}

If

\hat{c} = x \hat{a} + y \hat{b} + z (\hat{a} \times \hat{b}),

then

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 22 - Vector Algebra and 3D Geometry>EXERCISE>Q 20

If

\vec{a}, \vec{b}

and

\vec{c}

are non-coplanar vectors and

λ

is a real number, then

[λ (\vec{a} + \vec{b}) λ^{2} \vec{b} λ \vec{c}] = [\vec{a} \vec{b} + \vec{c} \vec{b}]

for