Question

State the condition (in terms of scalar / vector products) under which two vectors :
(i) A and B , are parallel to each other.
(ii) P and Q are perpendicular to each other.​

Answer 1

1)   A×B = 0     vector  product is zero

ii) A.B=0          scalar product is zero .

Answer 2

(I). If two vector are parallel then the cross product must be zero.

(II). If two vector are perpendicular then the dot product must be zero.

Explanation:

Given that,

(I). A and B are parallel to each other

We need to calculate the cross product

Using formula of cross product

When A || B, Then $\theta=0^{\circ}$

$A\times B=AB\sin\theta$

Put the value of angle

$A\times B=AB\sin0$

$A\times B=0$

If two vector are parallel then the cross product must be zero.

(II). P and Q are perpendicular to each other

We need to calculate the cross product

Using formula of dot product

When P ⊥ Q, Then $\theta=90^{\circ}$

$P\cdot Q=PQ\cos\theta$

Put the value of angle

$P\cdot Q=PQ\cos90$

$P\cdot Q=0$

If two vector are perpendicular then the dot product must be zero.

Hence, (I). If two vector are parallel then the cross product must be zero.

(II). If two vector are perpendicular then the dot product must be zero.

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Topic : vector and scalar

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