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Which of the ...

Question

Which of the following expressions does not make sense?
$u, v, w$ are vectors.

A

(u + v) \times (u - w)

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B

| u | \times (w - v)

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C

| u | (v \times w)

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D

u + (v - w)

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Solution

The correct option is B $| u | \times (w - v)$
$(u + v) \times (u - w), being cross product of two vectors. hence make sense.$
$| | u | | is scalar and (w-v) is vector. Cross product of scalar and vector does not make sense.$
$| | u | | (v \times w) is scalar multiple of vector. hence make sense.$
$u + (v - w) is addition and subtraction of vectors.Hence make sense.$

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\to u

\to v

are unit vectors such that

\to u \times \to v + \to u = \to w

\to w \times \to u = \to v,

then the value of

[\to u, \to v, \to w]

\vec{u,} \vec{v} and \vec{w}

be vectors such

\vec{u} + \vec{v} + \vec{w} = \vec{0} .

|\vec{u}| = 3, |\vec{v}| = 4 and |\vec{w}| = 5,

\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} .

u, v

w

be vectors such that

u + v + w = 0

| u | = 3, | v | = 4

| w | = 5

u . v + v . w + w . u

u, v

w

| u | = 1, | v | = 3

| w | = 2

. If the projection of

v

u

is equal to that of

w

u

v

w

are perpendicular to each other, then

| u - v + w |

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(\to u + \to v - \to w) . (\to u - \to v) \times (\to v - \to w)

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