Exercise 7.3 Solution FSc 2nd Year Math

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        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Notice (8): Undefined index: site_id [APP/Controller/PageprocessController.php, line 112]

Code Context

        {         
            $apikey = $this->request->data['api_key'];
            $siteid = $this->request->data['site_id'];

$apikey = null

PageprocessController::cdnurl() - APP/Controller/PageprocessController.php, line 112
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 491
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167
[main] - APP/webroot/index.php, line 117

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.3
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 13
PDF Size: 6.27 MB

In this exercise we will read these topics:

Scalar product of two vectors.
Define scalar and dot product.
Define the scalar product of vectors in a plane.
Define the scalar product of vectors in a space.
Define perpendicular vectors.
Show that the zero vector is perpendicular to every vector.
Properties of dot product.
Define the angle between two vectors.
Projection of a vector upon another.

[PDF Download]

Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13

Exercise 7.3 Solution FSc 2nd Year Math

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